Mathematically prove that all bodies heavy or light, reach the ground at the same time when dropped from the same time.

Open in App

Solution

$W h e n b o d y i s d r o p p e d, i t s i n i t i a l v e l o c i t y i s z e r o . u = 0 l e t s b e t h e d i s \tan c e t a r v e l l e d f r o m t h e h e i g h t t o g r o u n d . s = u t + \frac{1}{2} a t^{2} s = \frac{1}{2} a t^{2} I n f r e e f a l l m o t i o n, a c c e l e r a t i o i s e q u a l t o t h e a c c e l e r a t i o n d u e t o g r a v i t y a = g s = \frac{1}{2} g t^{2} t = \sqrt{\frac{2 s}{g}} w h e r e t i s t h e t i m e p e r i o d t a k e n b y t h e b o d y t o r e a c h t h e g r o u n d . T h i s e x p r e s s i o n o f t i m e p e r i o d i s i n d e p e n d e n t o f t h e m a s s o f t h e o b j e c t . S O h e a v y m a s s o r l i g h t m a s s t a k e s s a m e t i m e t o r e a c h t h e g r o u n d .$

Suggest Corrections

Similar questions

Q. Assertion :When a body is dropped or thrown horizontally from the same height, it would reach the ground at the same time. Reason: Horizontal velocity has no effect on the vertical direction

Q. Assertion :Two bodies of different masses dropped from the same height reach the ground at the same instant of time. Reason: Time of flight depends upon the mass of the bodies.

A light and a heavy body, both are dropped simultaneously from the same height. Which will strike the ground earlier ?

Q. When a body is dropped from same height on surface of the earth and the moon the ratio of time to reach the ground will be:

A ball P is dropped vertically and another ball Q is thrown horizontally with the some velocity from the same height and at the same time. If air resistance is neglected, then

Join BYJU'S Learning Program