A body, thrown upwards with some velocity reaches the maximum height of 50 m. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of:

Question

A body, thrown upwards with some velocity reaches the maximum height of 50 m. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of: (A) 100 m (B) 200 m (C) 300 m (D) 400 m

Tardigrade Admin · Accepted Answer

At maximum height, final velocity is zero.
From equation of motion, we have

v^{2} = u^{2} - 2 g h

Where

v

is final velocity,

u

is initial velocity,

h

is height and

g

is acceleration due to gravity.
Since body reaches maximum height in both cases, hence final velocity is zero.

∴ v = 0

\Rightarrow \frac{h _{1}}{h _{2}} = \frac{u _{1}^{2}}{u _{2}^{2}}

Given,

u_{2} = 2 u_{1}, v_{1} = u

∴ \frac{h _{1}}{h _{2}} = \frac{u ^{2}}{( 2 u ) ^{2}} = \frac{1}{4}

\Rightarrow h_{2} = 4 h_{1} = 4 \times 50

= 200 m

.
Note: Maximum height attained does not depend upon the mass of the body.

Q. A body, thrown upwards with some velocity reaches the maximum height of 50m. Another body with double the mass thrown up with double the initial velocity will reach a maximum height of:

100 m

200 m

300 m

400 m

Q. A body, thrown upwards with some velocity reaches the maximum height of $50 m$ . Another body with double the mass thrown up with double the initial velocity will reach a maximum height of: