Question

Two bodies A and B having mass $m$ and $3m$ are connected by a light string as shown in the figure. The observer is on the block B. Find the acceleration of the image of block B as seen by the observer. $($Consider that mass of the observer is negligible and there is no friction between block $A$ and the surface$)$

• A. $\frac{3g}{2}$ downwards
• B. $\frac{3g}{2}$ upwards
• C. $\frac{g}{2}$ upwards
• D. $\frac{g}{4}$ downwards

Answer 1

The correct option is B $\frac{3g}{2}$ upwards

FBD of block $B$:


$3mg-T=3ma----\left(1\right)$

FBD of block $A$:


$T=ma---\left(2\right)$

Adding (1) and (2),
$3mg=3ma+ma$
or $a=\frac{3g}{4}$ (downwards)

Then, acceleration of image of B will be :
$a_I=-\frac{3g}{4}$ (upwards)

Acceleration of image of B in plane mirror w.r.t B
$a_{IO}=a_I-a_O$
$=-\frac{3g}{4}-\frac{3g}{4}$
[taking downward +ve]
$=\frac{-3g}{2}$ (upwards)

Why this question? This question is application based problem where acceleration of image related concept is tested.