NCERT Class 11 Physics Solutions: Chapter 6 – Work, Energy, and Power Part 8

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Question 6.17:

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

The bob A of a pendulum released from 30° to the vertical hi …

Figure Shown How High Does the Bob a Rise After the Collisio …

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Answer:

Bob A will not rise at all

Explanation:

In an elastic collision between two equal masses in which one is stationary, while the other is moving with some velocity, the stationary mass acquires the same velocity, while the moving mass immediately comes to rest after collision. In this case, a complete transfer of momentum takes place from the moving mass to the stationary mass.

Hence, bob of mass m, after colliding with bob of equal mass, will come to rest, while bob will move with the velocity of bob at the instant of collision.

Question 6.18:

The bob of a pendulum is released from a horizontal position. If the length of the pendulum is 1what is the speed with which the bob arrives at the lowermost point, given that it dissipated of its initial energy against air resistance?

Answer:

Length of the pendulum,

Mass of the bob

Energy dissipated

According to the law of conservation of energy, the total energy of the system remains constant.

At the horizontal position:

Potential energy of the bob,

Kinetic energy of the bob,

Total energy

At the lowermost point (mean position):

Potential energy of the bob,

Kinetic energy of the bob,

Total energy,

As the bob moves from the horizontal position to the lowermost point, 5% of its energy gets dissipated.

The total energy at the lowermost point is equal to 95% of the total energy at the horizontal point, i.e.,

Question 6.19:

A trolley of mass carrying a sandbag of is moving uniformly with a speed of on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of. What is the speed of the trolley after the entire sand bag is empty?

Answer:

The sand bag is placed on a trolley that is moving with a uniform speed of The external forces acting on the system of the sandbag and the trolley is zero. When the sand starts leaking from the bag, there will be no change in the velocity of the trolley. This is because the leaking action does not produce any external force on the system. This is in accordance with Newton’s first law of motion. Hence, the speed of the trolley will remain

Question 6.20:

A body of mass travels in a straight line with velocity .where . What is the work done by the net force during its displacement from ?

Answer :

Mass of the body,

Velocity of the body is governed by the equation, with

Initial velocity,

Final velocity

Work done, Change in kinetic energy