Question

Two bodies A (of mass 1 kg) and (of mass 3 kg) are dropped from heights of 16 m and 25 m respectively. The ratio of the time taken by them to reach the ground is
a) 5/4
b) 12/5
c) 5/12
d) 4/5​

Answer 1

Question :

Two bodies A (of mass 1 kg) and (of mass 3 kg) are dropped from heights of 16 m and 25 m respectively. The ratio is of the time taken by them to reach the ground

a) 5/4

b) 12/5

c) 5/12

d) 4/5

To find :

The ratio of the time taken by them to reach the ground.

Solution :

From the equation :

$\sf \small \: h = ut + \frac{g {t}^{2} }{2}$

We get :

$\sf \small \: t = \sqrt{ \frac{2h}{g} }$

Just by putting initial velocity (u) = 0

As it is dependent on mass it is only dependent on height(h)

So the ratio of time will be the square root of their respective height i.e.

4:5

$\boxed{ \sf so \: \: the \: answer \: becomes \: 4 : 5 \: i.e \: option \: d}$

Answer 2

Answer:

solution:-

From the equation :

$\sf \small \: h = ut + \frac{g {t}^{2} }{2}h=ut+2gt2$

We get :

$\sf \small \: t = \sqrt{ \frac{2h}{g} }t=g2h$

Just by putting initial velocity (u) = 0As it is dependent on mass it is only dependent on height(h)So the ratio of time will be the square root of their respective height i.e.4:5

so, the answer becomes 4 : 5