First slide

Application of Newtons laws

Question

In the figure, a person wants to raise 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.

Moderate

A

(i)
B

(ii)
C

Same in both
D

Cannot be determined

Solution

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

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