Question

Consider the situation shown in figure. The elevator is going up with an acceleration of $2.00m/s^2$ and the focal length of the mirror is $12.0cm$. The entire surfaces are smooth and the pulley is light. The mass-pulley system is released from rest (with respect to the elevator) at $t=0$ when the distance of $B$ from the mirror is $42.0cm$. Find the distance (in cm) between the image of the block $B$ and the mirror at $t=0.200s$. Take $g=10m/s^2$.

Answer 1

Answer: 8.57

Consider observer in elevator.
Consider free body diagram. of blocks $A$ and $B$,

For motion of $A,T=m{a}_{\text{rel }}$...(1)
For motion of $B,mg+m{a}_0-T=m{a}_{\text{rel }}$..(2)
$(1)+(2)\Rightarrow mg+m{a}_0=2m{a}_{\text{rel }}$
$a_{\text{ rel }}=\frac{g+a_0}{2}$
Using, $S=ut+\frac{1}{2}a{t}^2$
$S=(0)(6)+\frac{1}{2}(6)(0.2{)}^2=12cm$
At $t=0.2\sec ,u=30cm,f=-12cm$
Using $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{v}+\frac{1}{30}=\frac{1}{-12}$
$\Rightarrow v=-\frac{30\times 12}{42}=-8.57cm$
$\therefore$ Required distance $=8.57cm$