Question

A cable in the form of a spiral rolls, as shown in the figure, has a linear density $0.25$ $kg/m$. It is uncoiled at a uniform speed of $2$ $m/s$. If the total length of the cable is $15$ $m$, the work done in uncoiling is (neglect friction) :

• A. 15 J
• B. 7.5 J
• C. 30 J
• D. 3.75 J

Answer 1

The correct option is B 7.5 J

The entire length of the cable has to be unrolled.
Mass of the cable : $M=Length\times Linearmassdensity=15\times 0.25=3.75kg$
Since the cable uncoils at uniform speed $v=2m/s$,
$W=\Delta KE=\frac{1}{2}M{v}^2=\frac{1}{2}\times 3.75\times 2^2=7.5Joule$