Question

A block of mass 10 kg is projected with speed 10 m/s on the surface of the plank of mass 10 kg, kept on smooth ground as shown in figure. Find out the velocity of two blocks when frictional force stops acting.

• A. 10 m/s, 5 m/s
• B. 10 m/s, 15 m/s
• C. 5 m/s, 5 m/s
• D. 10 m/s, 10 m/s

Answer 1

The correct option is C 5 m/s, 5 m/s

Initial velocity of block A is 10 m/s, and it will decrease after keeping it on B due the friction force between both the blocks.

Retardation of block A due friction (a ) = $-\mu g$

Velocity of A at any time t

$v_A=u+at$

$⟹v_A=10-\mu gt$; $\mu =0.1$ and $g=10m/s^2$

$⟹v_A=10-t$. . . . . .(1)

Acceleration of block B due friction (a ) = $\mu g$

−μ

Velocity of B at any time t

$v_B=u+at$

$⟹v_B=0+\mu gt$

$⟹v_B=t$. . . . . .(2)

Frictional force will stops working when both the block move the same velocity.

$v_A=v_B$

$⟹10-t=t$

$⟹t=5$ sec

By substituting value of t in equation 1 and equation, we get

$v_A=5$ m/s

$v_B=5$ m/s