Question

A block of mass $m_1$ lies on the top of fixed wedge as shown in Fig (a) and another block of same mass $m_1$ lies on top of wedge which is free to move as shown in Fig (b) . At time $t=0$ , both the blocks are released from rest from a vertical height $h$ above the respective horizontal surfaces on which the wedge is placed as shown. There is no friction between block and wedge in both the figures. Let $T_1$ and $T_2$ be the time taken by the blocks, respectively, to just reach the horizontal surface. Then

• A. $T_1>T_2$
• B. $T_1<T_2$
• C. $T_1=T_2$
• D. Data insufficient

Answer 1

The correct option is A $T_1>T_2$

In the (a) case acceleration of the "$m_1$" along the incline is $a_1=gsin\theta$
Whereas in the (b) case the acceleration of $"m_1"$ along the incline can be found by applying psuedo force on $"m_1"$ as shown.
So, the acceleratin $a_2=\frac{m_{1}g\sin \theta +m_{1}A\cos \theta }{m_1}$
hence $a_1<a_2$, so $T_1>T_2$

Therefore of option A is correct