Question

A light and smooth pulley is attached to the ceiling of a lift moving upward with acceleration $a_0=2{\text{m/s}}^2$ as shown in the figure. Two blocks of equal masses $(m=3\text{kg})$ are attached to the two ends of a massless string passing over the pulley. Find the tension in the string. (Take $g=10{\text{m/s}}^2$).

• A. $12\text{N}$
• B. $24\text{N}$
• C. $10\text{N}$
• D. $36\text{N}$

Answer 1

The correct option is D $36\text{N}$

From the frame of reference of lift, a pseudo force will act on both blocks in the direction opposite to the acceleration of lift. Let acceleration of blocks in frame of lift be $a{\text{m/s}}^2$


From F.B.D of both blocks, applying Newton's $2^{\text{nd}}$ law in the direction of acceleration:
$mg+m{a}_0-T=ma...\left(i\right)$
$T-mg-m{a}_0=ma...\left(ii\right)$
Substracting eqn $\left(i\right)$ from Eq. $\left(ii\right)$ gives,
$2T-2mg-2m{a}_0=0$
$\Rightarrow T=m(g+a_0)$
$\therefore T=3(10+2)=36\text{N}$