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>> $The pulley (figure) is fixed, light and$

Question

The pulley (figure) is fixed, light and smooth. The string is light and mass m < mass M. At t = 0, M and m are at rest, when the system is released. At time t = $t_{1}$ the mass 'M' is displaced by 'd'. The speed of the big block M at time $t_{1}$ with respect to the pulley is:

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A

$\frac{2 ( M + m ) g d}{M}$

B

$\frac{2 M g d}{M + m}$

C

$\frac{2 ( M - m ) d g}{M + m}$

D

$\frac{2 ( M - m ) d g}{M}$

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is C)

Let $a$ be the acceleration of the system as well as of the block of mass M.
for mass $M$ ,
$M a = M g - T . . . . (1)$
for mass $m$ ,
$m a = T - m g . . . . . (2)$
$(1) + (2), a = \frac{( M - m ) g}{( M + m )}$
now using the formula, $v^{2} - u^{2} = 2 a s$
here, $u = 0, s = d$ so , $v^{2} = 2 a d = \frac{2 ( M - m ) g d}{( M + m )}$
$∴ v = \frac{2 ( M - m ) g d}{( M + m )}$
Ans:(C)

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