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Velocity of COM

Two mass m an...

Question

Two mass m and 2m are attached with each other by a rope passing over a frictionless and massless pulley. If the pulley is accelerated upwards with an acceleration 'a' , what is the value of tension ?

\frac{g + a}{3}

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\frac{g - a}{3}

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\frac{4 m (g + a)}{3}

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\frac{m (g - a)}{3}

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Solution

The correct option is A $\frac{4 m (g + a)}{3}$
$\begin{matrix} let, with relative to pulley the block 2 m descends with acceleration a_{0} for 2 m mass 2 m (a - a_{0}) = T - 2 m g - (1) \end{matrix}$

$\begin{matrix} for m mass m (a + a_{0}) = T - m g_{0} - (2) -from (1) & (2) 2 m a - 2 m a_{0} = T - 2 m g 2 m a + 2 m a_{0} = 2 T - 2 m g \end{matrix}$

$\begin{matrix} 4 m a = 3 T - 9 m g on T = \frac{4 m (a + q)}{z} \end{matrix}$

Option: C

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Two mass m and 2m are attached with each other by a rope passing over a frictionless and massless pulley. If the pulley is accelerated upwards with an acceleration 'a' , what is the value of tension ?

The correct option is A 4m(g+a)3 let, with relative to pulley the block 2 m descends with acceleration a0 for 2 m mass 2m(a−a0)=T−2mg−(1) for m mass m(a+a0)=T−mg0−(2) -from (1)&(2)2ma−2ma0=T−2mg2ma+2ma0=2T−2mg 4ma=3T−9mg on T=4m(a+q)z Option: C