Question

$\large\dag \sf \: Question :-$
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Two objects of masses m1 and m2 having the same size are dropped simultaneously from heights h1 and h2 respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if
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(i) one of the objects is hollow and the other one is solid
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(ii) bothof them are hollow, size remaining the same in each case. Give reason?
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Answer 1

Question :-

Two objects of masses m1 and m2 having the same size are dropped simultaneously from heights h1 and h2 respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if

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(i) one of the objects is hollow and the other one is solid

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(ii) bothof them are hollow, size remaining the same in each case. Give reason?

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Solution :-

$\sf \: = As \: the \: two \: masses \: are \: dropped, \: u = 0, a = g \\ \sf(which \: does \: not \: depend \: upon \: mass)$

$\sf \: = from \: s = ut + \frac{1}{2} {at}^{2}$

$\sf \: = h_{1} = 0 + \frac{1}{2} {gt}^{2} _{1} \: and \: h_{2} = 0 + \frac{1}{2} {gt}^{2} _{2}$

$\sf \: = \frac{h1}{h2} = \left ( \begin{array}{ccc} \frac{t1}{t2} \end{array}\right)^{2} or \: \frac{t1}{t2} = \sqrt{ \frac{h1}{h2} }$

$\sf \: this \: ratio \: of \: time \: should \: remain \: same \: if \:$

(i)one of the objects is hollow and the other one is solid - as the ratio is independent of masses.

(ii) both the objects are hollow, as acceleration due is gravity (g) does not depent upon mass and also whether the body is hollow/solid. As size remains the same in each case, there is no effect of resistance due to air in the two cases.