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  4. In the figure, a person wants to rise a block lying on the ground to a height h. In both the cases, if the time required is same, then in which case he has to exert more force? Assume pulleys and strings light.

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Q. In the figure, a person wants to rise a block lying on the ground to a height $h$. In both the cases, if the time required is same, then in which case he has to exert more force? Assume pulleys and strings light.Physics Question Image

Laws of Motion

Solution:

Since, $h=\frac{1}{2} a t^{2}, a$ should be same in both cases, because $h$ and $t$ are same in both cases as given.
In Fig. (a), $F_{1}-m g=m a$
$\Rightarrow F_{1}=m g+m a$
In Fig. (b), $2 F_{2}-m g=m a$
$\Rightarrow F_{2}=\frac{m g+m a}{2}$
$\therefore F_{1}>F_{2}$

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