Question

If wedge is moving with acceleration as shown in the figure and friction coefficient between two blocks is $\mu$ then value of net force on $m$ is

• A. $ma$
• B. $\sqrt{2}ma$
• C. $mg-\mu ma$
• D. $zero$

Answer 1

Answer: (B)

$\sqrt{2}ma$

Both blocks $M$ and $m$ will move in same direction with acceleration $a$ in horizontal direction.

$N=ma$...(i)

Now analysing motion of $m$ in frame of reference of $M$, It will have only downward acceleration due to gravitational force, and pseudo force $ma$ will act in left direction

From constraint relation $a_M=a_m=$ $a$ in downward direction.

$mg-f-T=ma$....(ii) in downwards direction,

where $f$ is frictional force and $T$ is tension in the string

Now the net force on $m$ from equation (i) and (ii) is

$F=\sqrt{(ma{)}^2+(ma{)}^2}=\sqrt{2}ma$