Class XI-XII Tuition (PUC) Updates

Given figures 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 some physical contexts for which these potential energy shapes are relevant.

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:

(a) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket,

(b) Work done by gravitational force in the above case,

(c) Work done by friction on a body sliding down an inclined plane,

(d) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity,

(e) Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

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 coefficient of kinetic friction = 0.1. Compute the

(a) Work done by the applied force in 10 s

(b) Work done by friction in 10 s

(c) Work done by the net force on the body in 10 s

(d) Change in kinetic energy of the body in 10 s and interpret your results.

Point out the correct alternative:
(a) When a conservative force does positive work on a body, the potential energy of the body increases/decreases/remains unaltered.
(b)Work done by a body against friction always results in a loss of its kinetic/potential energy.
(c) The rate of change of total momentum of a many particle system is proportional to the external force/sum of the internal forces of the system.
(d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the system of two bodies.

The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. How high does the bob A rise after the collision? Neglect the size of the bobs and assume the collision to be elastic.

In elastic collision the linear momentum is conserved .
linear momentum =mass x velocity =mv

here mass of A and B are same.

so if elastic collision occur then A bobs complete transfer it momentum on bobs B.their velocities interchanged 

After collision A will come to rest and B moves with velocity of A.thus bob A would not rise after collision.

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?

A particle of mass 0.5 kg travels in a straight line with velocity u = a x^3/2, where a = 5 m^-1/2 s^-1. What is the work done by the net force during its displacement from x = 0 to x = 2 m?

Which of the following potential energy curves in Fig. cannot possibly describe the elastic collision of two billiard balls? Here r is distance between centres of the balls.

Consider the decay of a free neutron at rest: n > p + e^–. Show that the two body decay of this type must necessarily give an electron of fixed energy, and therefore, cannot account for the observed continuous energy distribution in the β -decay of a neutron or a nucleus, Fig.

A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a friction less track. After a while, sand starts leaking out of a hole on the trolley’s floor at the rate of 0.05 kg s^-1. What is the speed of the trolley after the entire sand bag is empty?