Question

A block can slide on a smooth inclined plane of inclination $\theta$, kept on the floor of a lift. When the lift is descending with a retardation a, the acceleration of the block relative to the incline is:

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

Answer 1

Answer: (A)

$(g+a)sin\theta$

Let the acceleration of the block kept on an incline is $b$ and its mass is m.

Since the lift is retarding downwards with a magnitude a, a pseudo force will be applied on the block in downward direction as shown in the fbd.
$(ma+mg)sin\theta =mb$
$b=(a+g)sin\theta$