## NCERT Solutions Class 11 Physics Chapter 6 Work, Energy and PowerThis article contains solution for all the NCERT Physics Class XI Chapter 6 questions. All solutions are written in detail for better understanding and in simple language. In order to help students become well - prepared in the subjects presented in this chapter, the textbook provides answers to worksheets, supplementary questions, sample problems, and other questions. Additionally, they aid in improving their capacity to respond to tricky, complicated questions in tests and other competitive assessments. Students can get a quick overview of the key terminology and concepts that are utilised in this chapter by consulting the NCERT Solutions for Class 11 Physics, which have been updated in accordance with the most recent CBSE Syllabus 2022-23. In our daily lives, words like "effort," "energy," and "power" are employed. A person is considered to be doing their work if they are lugging bricks, sowing seeds, studying for examinations, etc. Work has a clear and defined definition in physics. ## NCERT Solutions for Class 11 Physics Chapter 6
The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative. - Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
- Work done by the gravitational force in the above case.
- Work done by friction on a body sliding down an inclined plane.
- Work done by an applied force on a body moving on a rough horizontal plane with uniformvelocity.
- Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.
- It is obvious that the force and displacement are moving in the same direction, meaning that the effort done on it is productive.
- It should be noticed that the object is moving upward, whilst the force of gravity is pulling the object downward. As a result, the work is detrimental.
- It is obvious that the object is moving in the opposite direction from where the frictional force is acting. As a result, the work is unfavourable.
- The frictional force acting on an object travelling in an uneven horizontal plane is directed in the opposite direction from the direction of the motion. A uniform force is supplied to the item in order to keep it moving at the same speed. As a result, the object is moving in the same direction as the force being applied. The task completed is therefore fruitful.
- It should be noticed that the bob is moving in the opposite direction from the air's resistance to it. As a result, the work is unsuccessful.
A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with the coefficient of kinetic friction = 0.1. Compute the - work done by the applied force in 10 s.
- work done by friction in 10 s.
- work done by the net force on the body in 10 s.
- change in kinetic energy of the body in 10 s.
Mass of the body = 2 Kg Horizontal force applied = 7 N Co - efficient of kinetic friction = 0.1 Acceleration produced by the applied force is, Change in Kinetic Energy = 635 - 0 = 635 J Thus, the work done by the net force is equal to the final kinetic energy.
Given in the figure are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case, specify the regions, if any, in which the particle cannot be found for the given energy. Also, indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.
The total energy is given by E = K.E + P.E K.E = E - P.E. Kinetic energy is always positive. The region where K.E. would turn negative prevents the particle from existing. (a) Potential energy is 0 for the region between x = 0 and x = a. Kinetic energy is therefore positive. The potential energy is greater than E for x > a. As a result, kinetic energy is zero. Therefore, the particle won't be present in the region where x > a. In this situation, the particle can have no total energy at all. (b) If P.E. > E along the entire x - axis, the object's kinetic energy would be negative. As a result, the particle won't be present here. (c) Because the P.E. is bigger than the E in this case (x = 0 to x = a and x > b), the kinetic energy is negative. In this area, the object is unable to be there. (d) For the ranges of x = a/2 to b/2 and x = a/2 to - b/2. Positive kinetic energy exists, and the P.E. This area contains the particle.
The potential energy function for a particle executing linear simple harmonic motion is given by V(x) = kx
Particle energy E = 1 J K = 0.5 N m
Answer the following:
Friction causes the casing to burn up, reducing the mass of the rocket. According to the principle of energy conservation: The decreased mass of the rocket will result in a decrease in total energy. As a result, the rocket provides the energy required for the casing to burn.
Gravitational force is a conservative force. The conservative force exerts no effort on a closed path. As a result, the gravitational force does zero work for each whole circle of the comet.
Since the system's overall energy should remain constant, the kinetic energy increases as the potential energy of the satellite rotating around the Earth diminishes. The satellite's velocity rises as a result. Despite this, atmospheric friction causes a slight reduction in the system's overall energy.
mass = 20 kg Displacement of the object, s = 4 m Work = F × s × cos θ θ = angle between the force and displacement F W = m × g = 20 × 4 × 9.8 × cos 90° = 0 [Because cos 90° = 0]
Mass. m = 20 kg Distance, s = 4 m The applied force direction is the same as the direction of the displacement. Therefore the angle between the force and displacement is zero degrees. Since,cos 0° = 1 ∴ W = F × s × cos θ = m × g = 20 × 4 × 9.8 × cos 0° = 784 J Thus the amount of work done is greater in scenario II.
Underline the correct alternative :
Decreases When a body is moved in the direction of the force, the conservative force exerts positive work on the body, which causes the body to travel to the centre of the force. As a result, the distance between the two gets smaller, and the body's potential energy gets smaller.
Kinetic energy When work is done in the direction that is counter to the direction of friction, the body's velocity is reduced. As a result, the kinetic energy drops.
External force Regardless of their directions, internal forces cannot result in a change in momentum. As a result, the change in overall momentum is proportional to the force acting on the system from outside.
Total linear momentum. The total linear momentum is unaffected by whether the impact is elastic or inelastic.
False Both bodies' energy and momentum are conserved and not separately.
False The external factors acting on the system have the power to influence the body and alter its energy.
False In a closed loop, the conservative force exerts no work on the moving body.
True
Answer carefully, with reasons:
In an elastic collision, the kinetic energy at the start and at the end is equal. There is no kinetic energy conservation when the two balls contact. It transforms into kinetic energy.
In an elastic collision, the system's entire linear momentum is conserved.
In an inelastic collision, kinetic energy will be lost. Always, the K.E. following a collision is lower than the K.E. initially. In an inelastic collision, the system's overall linear momentum is also conserved.
Because the forces involved are conservative forces, the collision is elastic. It is based on how far apart the billiard balls' centres are from one another.
A body is initially at rest. It undergoes one - dimensional motion with constant acceleration. The power delivered to it at time t is proportional to: - t
^{1/2} - t
^{3/2} - t
^{2} - t
A body is initially at rest. It undergoes one - dimensional motion with constant accelerration. P = Fv Where,P = power,F = force,v = velocity Using equation of motion, v = u + at where, v = final velocity, u = initial velocity, a = acceleration, t = time The fact that the body is initially at rest and has zero initial velocity is given (the body is not moving at all). u = 0. v = 0 + at v = at Force is the product of mass and acceleration F = ma Therefore Power becomes, P = Fv P = Fv P = ma × at P = ma In this case, acceleration and mass are both constants. Power therefore has a direct relationship with time. Therefore, P is directly proportional to t
A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to: - t
^{1/2} - t
^{3/2} - t
^{2} - t
The power of the body can be calculated as, P = [F][v] By substituting the dimension values of F and v in the above equation, we get P = [MLT The values of power and mass will remain constant since the body is moving while being acted upon by a source of constant power. Consequently, the above equation may be expressed as, [L L Therefore,L is directly proportional to T
A body constrained to move along the z - axis of a coordinate system is subject to a constant forceF given by where i, j, k, are unit vectors along the x - y - and z - axis of the system, respectively. What is the work done by this force in moving the body at a distance of 4 m along the z - axis?
The constant force applied on a body is, The body is at a distance of 4 m, away from the origin and is moving along the z - axis. Therefore, the displacement vector of the body at this particular instant would be, The work done in moving the object by the force would be given by, Substituting values in the above equation we get, So the work done by the force in moving the object 4 m along the direction of z axis is 12 J.
An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with 100 keV. Which is faster, the electron or the proton? Obtain the ratio of their speeds. (electron mass = 9.11 × 10
Mass of the electron,m Mass of the proton,m
A raindrop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to the viscous resistance of the air) until, at half its original height, it attains its maximum (terminal) speed and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is 10 ms
Radius of the rain drop,r = 2 mm = 2 × 10 Height from which the rain drop is falling,s = 500 m Density of the water,ρ = 10
A molecule in a gas container hits a horizontal wall with speed 200 m s
We know that in an inelastic collision, the momentum is always conserved. The molecule approaches and rebounds with the same speed i.e. 200 m/s. ∴ Initial Velocity = Final Velocity = 200 m/s Therefore the initial kinetic energy is given by,
A pump on the ground floor of a building can pump up water to fill a tank of volume 30 m
The volume of the tank = 30 m Time taken to fill the tank = 15 minutes = 15 × 60 = 900 seconds Height of the tank above the ground = 40 m Efficiency of the pump,η = 30% Density of the water,ρ = 10
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head - on by another ball bearing of the same mass moving initially with speed V. If the collision is elastic, which of the following figure is a possible result after collision?
Mass of the ball bearing is m. Total Kinetic Energy of the system before collision is,
A ball A which is at an angle 30° to the vertical is released, and it hits a ball B of the same mass, which is at rest. Does ball A rise after collision? The collision is an elastic collision.
Ball B acquires the velocity of ball A when it collides with ball B, which is stationary, in an elastic collision, while ball A immediately comes to rest following the contact. Momentum is transferred from the stationary body to the moving body. Ball B moves with the velocity of ball A as a result, and ball A comes to rest after the contact.
The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1.5 m, what is the speed with which the bob arrives at the lowermost point, given that it dissipated 5% of its initial energy against air resistance?
Length of the pendulam,l = 1.5 m Potential energy of the bob at the horizontal position = mgh = mgl The initial energy lost as a result of air resistance when the bob descends from horizontal to its lowest point is 5%. The bob's total kinetic energy is equal to 95% of its total potential energy in its horizontal position.
A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg s
The sandbag is put onto the trolley, which is moving at a constant speed of 27 km/h. There is no system of external forces at work. There won't be any outside force acting on the system, even if the sand begins to leak out of the bag. As a result, the trolley's speed won't change. It will be 27 kilometres per hour.
A body of mass 0.5 kg travels in a straight line with velocity v = ax
Mass of the body,m = 0.5 Kg Velocity of the body,v = ax Here,acceleration a = 5 m Initial velocity at x = 0,
The windmill sweeps a circle of area A with its blades. If the velocity of the wind is perpendicular to the circle, find the air passing through it in time t and also the kinetic energy of the air. 25 % of the wind energy is converted into electrical energy, and v = 36 km/h, A = 30 m
Density of air,ρ kg/m Time taken = t sec Velocity of air = v m/s
A person trying to lose weight (dieter) lifts a 10 kg mass one thousand times to a height of 0.5 m each time. Assume that the potential energy lost each time she lowers the mass is dissipated. (a) How much work does she do against the gravitational force? (b) Fat supplies 3.8 × 10
Mass of the person,m = 10 Kg Height to which the mass is lifted,h = 0.5 m Number of times,n = 1000 (a) Work done against gravitational force.
A family uses 8 kW of power. (a) Direct solar energy is incident on the horizontal surface at an average rate of 200 W per square meter. If 20% of this energy can be converted to useful electrical energy, how large an area is needed to supply 8 kW? (b) Compare this area to that of the roof of a typical house.
(a) Power used by the family, Percentage of energy converted to useful electrical energy = 20% As solar energy is incident at a rate of 200 Wm The area required to generate the desired energy is A. Useful electrical energy produced per second, (b) The area needed is comparable to the roof of a large house of dimension 14m × 14m.
A bullet of mass 0.012 kg and horizontal speed 70 m s
Mass of bullet,m Initial speed of the bullet,u Mass of the wooden block,m Initial speed of the wooden block,u Final speed of the system of the bullet and the block = v m/s Applying the law of conservation of momentum, Let h be the height to which the block rises. Applying the law of conservation of energy to this system, Potential energy of the combination = Kinetic energy of the combination The wooden block will rise to a height of 0.212m. The heat produced = Initial kinetic energy of the bullet - final kinetic energy of the combination
Two inclined frictionless tracks, one gradual and the other steep, meet at A, from where two stones are allowed to slide down from rest, one on each track. Will the stones reach the bottom at the same time? Will they reach there at the same speed? Explain. Given θ
In the figure, the sides AB and AC are inclined to the horizontal at ∠θ According to the law of conservation of mechanical energy, Potential Energy at the top = Kinetic Energy at the bottom Since the height of both sides is the same, both stones will reach the bottom at the same speed. From (1) and (2), we get v Hence, both stones will reach the bottom at the same speed. For the stone 1 Net force acting on the stone is given by,
A 1 kg block situated on a rough incline is connected to a spring of spring constant 100 N m
Mass of the block,m = 1 Kg Spring constant,k = 100 N m Displacement in the block,x = 10 cm = 0.1 m At equilibrium,
A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down with a uniform speed of 7 ms
Mass of the bolt,m = 0.3 Kg Potential Energy of the bolt = mgh = 0.3 × 9.8 × 3 = 8.82 J The bolt doesn't bounce back. Therefore, all of the potential energy is transformed into heat energy. Since the acceleration due to gravity is the same in all inertial systems, the heat generated will not change even if the lift is motionless.
On a frictionless track, a trolley moves with a speed of 36 km/h with a mass of 200 Kg. A child whose mass is 20 kg runs on the trolley with a speed of 4 m/s from one end to another, which is 20 m. The speed is relative to the trolley in the direction opposite to its motion. Find the final speed of the trolley and the distance the trolley moved from the time the child began to run.
Mass of the trolley,m = 200 Kg Speed,v = 36 Km/h = 10 m/s Mass of the boy = 20 Kg
Which of the following does not describe the elastic collision of two billiard balls? The distance between the centres of the balls is r.
(i), (ii), (iii), (iv) and (vi). In a system, the distance between any two masses has an inverse relationship with their potential energy. As the two balls approach closer to one another, the potential energy of the system will decrease. The potential energy zeroes out when the balls collide, or when r = 2R. These requirements are not met by the potential energy curve in (i), (ii), (iii), (iv), and (vi). There is therefore no elastic collision. |