Question

A block is placed on the top of a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation $a$, the block is released. The acceleration of the block relative to the incline is

• A. $g\sin \theta$
• B. $a\sin \theta$
• C. $(g-a)\sin \theta$
• D. $(g+a)\sin \theta$

Answer 1

The correct option is D $(g+a)\sin \theta$

When the lift is descending with a retardation $($ negative acceleration$)a,$ the effective value of $g$ is $g_{eff}=g+a$

the component of this acceleration along the inclined plane is

$g_{eff}\sin \theta =\left(g+a\right)\sin \theta$

Hence,

option $\left(D\right)$ is correct answer.