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18
MCQ (Single Correct Answer)

A cricket ball of mass 150 g moving with a speed of $$126 \mathrm{~km} / \mathrm{h}$$ hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001 s , the force that the batsman had to apply to hold the bat firmly at its place would be

A
10.5 N
B
21 N
C
1.05 $$\times$$ 10$$^4$$ N
D
2.1 $$\times$$ 10$$^4$$ N
19
MCQ (Multiple Correct Answer)

A man of mass $$m$$, standing at the bottom of the staircase, of height $$L$$ climbs it and stands at its top.

A
Work done by all forces on man is equal to the rise in potential energy mgL
B
Work done by all forces on man is zero
C
Work done by the gravitational force on man is mgL
D
The reaction force from a step does not do work because the point of application of the force does not move while the force exists
20
MCQ (Multiple Correct Answer)

A bullet of mass $$m$$ fired at $$30^{\circ}$$ to the horizontal leaves the barrel of the gun with a velocity $$v$$. The bullet hits a soft target at a height $$h$$ above the ground while it is moving downward and emerge out with half the kinetic energy it had before hitting the target.

Which of the following statements are correct in respect of bullet after it emerges out of the target?

A
The velocity of the bullet will be reduced to half its initial value
B
The velocity of the bullet will be more than half of its earlier velocity
C
The bullet will continue to move along the same parabolic path
D
The bullet will move in a different parabolic path
E
The bullet will fall vertically downward after hitting the target
F
The internal energy of the particles of the target will increase
21
MCQ (Multiple Correct Answer)

Two blocks $$M_1$$ and $$M_2$$ having equal mass are free to move on a horizontal frictionless surface. $$M_2$$ is attached to a massless spring as shown in figure. Initially $$M_2$$ is at rest and $$M_1$$ is moving toward $$M_2$$ with speed $$v$$ and collides head-on with $$M_2$$.

A
While spring is fully compressed all the KE of $$M_1$$ is stored as PE of spring
B
While spring is fully compressed the system momentum is not conserved, though final momentum is equal to initial momentum
C
If spring is massless, the final state of the $$M_1$$ is state of rest
D
If the surface on which blocks are moving has friction, then collision cannot be elastic
22
Subjective

A rough inclined plane is placed on a cart moving with a constant velocity $$u$$ on horizontal ground. A block of mass $$M$$ rests on the incline. Is any work done by force of friction between the block and incline? Is there then a dissipation of energy?

Explanation

Consider the adjacent diagram. As the block M is at rest.

Hence, f = frictional force = $$Mg\sin\theta$$

The force of friction acting between the block and incline opposes the tendency of sliding of the block. Since, block is not in motion, therefore, no work is done by the force of friction. Hence, no dissipation of energy takes place.