A mass of 2 kg 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. Find the mass M. (in kg)

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Detailed Solution

The tension in the string is given by $T = \frac{mM}{m + M} g$
In the second case M changes to 2M and T changes to T
Dividing (i) by (ii), we get
$\frac{2}{3} = \frac{m + 2 M}{m + M} \times \frac{1}{2}$
Substituting m = 2 kg, then M = 1 kg

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