A weightless string passes through a slit over a pulley. The slit offers frictional force $f$ to the string. The string carries two weights having masses $m_{1}$ and $m_{2}$ where $m_{2} > m_{1}$ , then acceleration of the weights is:

\frac{{(m}_{2} - m_{1}) g - f}{m_{1} + m_{2}}

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\frac{f - ({(m}_{2} - m_{1}) g}{{(m}_{1} + m_{2})}

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\frac{{(m}_{1} + m_{2}) g - f}{m_{1} - m_{2}}

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\frac{m_{2} g - f}{{(m}_{1} + m_{2})}

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Solution

The correct option is A $\frac{{(m}_{2} - m_{1}) g - f}{m_{1} + m_{2}}$
From FBD,
for mass $m_{1}$ , $m_{1} a = T - m_{1} g . . . . . . (1)$
for mass $m_{2}$ , $m_{2} a = m_{2} g - T - f . . . . (2)$
$(1) + (2), (m_{1} + m_{2}) a = (m_{2} - m_{1}) g - f$
$∴ a = \frac{(m_{2} - m_{1}) g - f}{(m_{1} + m_{2})}$

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A weightless string passes through a slit over a pulley. The slit offers frictional force f to the string. The string carries two weights having masses m1 and m2 where m2>m1, then acceleration of the weights is:

The correct option is A (m2−m1)g−fm1+m2From FBD,for mass m1, m1a=T−m1g......(1)for mass m2, m2a=m2g−T−f....(2)(1)+(2),(m1+m2)a=(m2−m1)g−f∴a=(m2−m1)g−f(m1+m2)

A weightless string passes through a slit over a pulley. The slit offers frictional force $f$ to the string. The string carries two weights having masses $m_{1}$ and $m_{2}$ where $m_{2} > m_{1}$ , then acceleration of the weights is: