2 bodies of different masses (one light the other heavy) are thrown vertically upwards with same initial speed which will rise to a greater height?justify

Open in App

Solution

Dear student
If we ignore air resistance then both will rise to the same height.
However if we take air resistance into our account then the heavier body will rise more than the lighter one.
Here is the explanation $l e t m < M t h e f o r c e o f a i r r e s i s \tan c e i s \vec{F} = - b \vec{V} w h e r e b i s c o n s \tan t a n d \vec{V} i s v e l o c i t y t h e e q u a t i o n o f m o t i o n w h i l e m o v i n g u p w a r d i s m a_{1} = m g + b V_{1} o r, a_{1} = g + \frac{b}{m} V_{1} a n d M a_{2} = M g + b V_{2} o r, a_{2} = g + \frac{b}{M} V_{2} a_{1} a n d a_{2} a r e t h e r e t a r d a t i o n s o f m a n d M w h i l e g o i n g u p w a r d W h e n b = 0 i . e . n o a i r r e s i s \tan c e, a_{1} = a_{2} = g, h e n c e b o t h w i l l r i s e s a m e h e i g h t . N o w m < M t h e r e f o r e a_{1} > a_{2} (\sin c e i n i t i a l l y V_{1} = V_{2} a t t h e t i m e o f p r o j e c t i o n) H e n c e, r e t a r d a t i o n s o f m w i i l b e m o r e t h a n M . H e n c e, h e a v i e r b o d y w i l l r i s e m o r e u n d e r a i r r e s i s \tan c e . R e g a r d s$

Suggest Corrections

Similar questions

Q. Consider the following statements A and B and identify the correct answer.
A) Two balls of different masses are thrown vertically upwards with the same initial velocity. They rise to the same maximum height above the ground.
B) Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projection in their downward motion with the same speed. (neglect air resistance)

Two bodies are thrown simultaneously from a tower with same initial velocity $v_{0}$ one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is.

Q. Two balls of different masses are thrown vertically upward with the same speed. then the gravitational force acting on them will be same. (neglect air resistance).

Q. A heavy stone is thrown from a cliff of height h with a speed v. The stoen will hit the ground with maximum speed if it is thrown
(a) vertically downward
(b) vertically upward
(c) horizontally
(d) the speed does not depend on the initial direction.

A body is thrown vertically upwards and rises to a height of 10m. The velocity with which the body was thrown upwards is : (g = 9.8 $m / s^{2}$ )

Join BYJU'S Learning Program