Question

A mass of $2kg$ hangs freely at the end of a string, which passes over a smooth pulley fixed at the edge of a smooth table. The other end of the string is attached to a mass $M$ on the table. If the mass on the table is doubled the tension in the string increases by one-half. The mass $M$ is :

• A. $5kg$
• B. $3.5kg$
• C. $1kg$
• D. $4.2kg$

Answer 1

The correct option is C $1kg$

The tension in the string is given by,

$T=\frac{mM}{m+M}g$ ..........(1)

In the second case, $M$ changes to $2M$ and $T$ changes to

$\left(\frac{3}{2}\right)T$

Therfore,

$\frac{3}{2}T=\frac{mM}{m+M}g$ ............(2)

Dividing (1) by (2), we get

$\frac{2}{3}=\frac{m+2M}{m+M}\times \frac{1}{2}$

That is

Mass, $M=1kg$