Question

A block of mass $m$ is suspended by a light thread from an elevator. The elevator is accelerating upward with uniform acceleration $a$. The work done during $t$ secs by the tension in the thread is:

• A. $\frac{m}{2}(g+a)a{t}^2$
• B. $\frac{m}{2}(g-a)a{t}^2$
• C. $\frac{m}{2}ga{t}^2$
• D. zero.

Answer 1

Answer: (A)

$\frac{m}{2}(g+a)a{t}^2$

Let our frame of reference be elevator, a pseudo force will act downwards
Total tension force acting on mass $m$ will be $m(g+a)$ in upward direction as mass $m$ is at rest wrt elevator i.e
$T$=$m(g+a)$
Displacement in upward direction during time $t$=$1/2a$$t^2$
Work done by tension force = $T$$\times$$displacement$
= $m(g+a)\times \frac{1}{2}a{t}^2$
=$\frac{m(g+a)a{t}^2}{2}$