QJEEM21Ph66d8: JEE Main 2021 Physics - Class 11 JEEM21Ph66d8 Solution: A block of mass m slides on the wooden wedge, which in turn…

Let acceleration of wedge is a_w and acceleration of block w.r.t. wedge is a_b

For the wedge w.r.t. ground


N cos60 $^\circ$ = Ma_w = 16a_w

$\Rightarrow$ N = 32a_w

F.B.D. of block w.r.t. wedge


Balancing vertical forces

N = 8g cos30 $^\circ$ $-$ 8a_w sin30 $^\circ$ $\Rightarrow$ 32a_w = 4 $\sqrt 3$ g $-$ 4a_w

$\Rightarrow$ a_w = ${{\sqrt 3 } \over 9}$ g

Along incline plane

8g sin30 $^\circ$ + 8a_w cos30 $^\circ$ = ma_b = 8a_b

a_b = g $\times$ ${1 \over 2} + {{\sqrt 3 } \over 9}$ g . ${{\sqrt 3 } \over 2} = {{2g} \over 3}$

Option (d)