Question

A block of mass $1\text{kg}$ is placed on a rough wedge which is fixed on an elevator going upwards with acceleration $2{\text{ms}}^{-2}$.The block is at rest with respect to the wedge. Select the correct option(s): (Take $g=10{\text{ms}}^{-2}$).

• A. Normal reaction force on the block is $6\sqrt{3}\text{N}$.
• B. Net reaction force acting on the block is $12\text{N}$.
• C. Net force on the block is zero.
• D. Net force on the block is $2\text{N}$.

Answer 1

Answer: (A), (B), (D)

Net force on the block is $2\text{N}$.

FBD of the block in the elevator frame of reference is given below where $ma$ is the pseudo force assumed in downward direction.


From the FBD,
$N=m(g+a)\cos {30}^{\circ }$
$=12.\frac{\sqrt{3}}{2}=6\sqrt{3}\text{N}$
Since the block is at rest,
$f=m(g+a)\sin {30}^0=6\text{N}$

Therefore, net reaction force $F=m(g+a)=12\text{N}$

Because the block is accelerated vertically upwards,
Net force on the block in ground frame $=ma$ (upwards)
$=1\times 2=2\text{N}$

Hence, options (a), (c) & (d) are correct.