First slide

Application of Newtons laws

Question

Two masses M and M/2 are joined together by means of light inextensible string passes over a frictionless pulley as shown in figure. When bigger mass is released, the small are will ascend with an acceleration of

Moderate

A

g
B

g/2
C

g/3
D

2g

Solution

Given, the mass of the heavier object,m1 M = and
the mass of the light object,m² =M/2.
Now, we have acceleration,
$a = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) g . . . . . (i)$
Putting these values in Eq. (i), we get
$\begin{array}{l} a = \frac{(M - \frac{M}{2})}{M + \frac{M}{2}} g \\ = (\frac{\frac{2 M - M}{2 M}}{\frac{2 M}{2}}) g \\ = \frac{g}{3} \end{array}$

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