Question

A cable in the form of a spiral roll (shown in the figure) has a linear density $\rho$. It is uncoiled at a uniform speed $v$. If the total length of the cable is $L$. The work done in uncoiling the cable is :-

• A. $\rho L{v}^2/4$
• B. $\rho L{v}^2/2$
• C. $\rho L{v}^2/3$
• D. $\rho L{v}^2$

Answer 1

Answer: (B)

$\rho L{v}^2/2$

Initial speed of the coil is $0m/s$
Final speed $=v$ (uncoiling speed)
Mass of the coil $=\rho L$
Thus, work done
$W=△KE=K_f-K_i$
$=\frac{1}{2}\times \left(\rho L\right)(v{)}^2-0=\frac{1}{2}\rho L{v}^2$.