A stone of mass 2 kg is projected upward with the kinetic energy of 98 J . The height at which the kinetic energy of the stone becomes half of its original value is given by

Question

A stone of mass 2 kg is projected upward with the kinetic energy of 98 J . The height at which the kinetic energy of the stone becomes half of its original value is given by (A) 5m (B) 2.5m (C) 1.5 m (D) 0.5 m

Tardigrade Admin · Accepted Answer

At the time of projection kinetic energy of the stone,

K = \frac{1}{2} mu^{2}

where m is the mass of the stone and u is the velocity of the projection
where

m

is the mass of the stone and

u

is the velocity of the
projection
or

u^{2} = \frac{2 K}{m} = \frac{2 \times 98}{2} = 98

U sin g, v^{2} = u^{2} - 2 g h

∴ h = \frac{u ^{2}}{2 g} (∵ v = 0)

h = \frac{98}{2 \times 9.8} = 5 m

Also,

K = \frac{1}{2} m (2 g h)

(Using

K^{'} = \frac{1}{2} m v^{'2} = \frac{1}{2} m \times (2 g h^{'})

∴ \frac{K ^{'}}{K} = \frac{h ^{'}}{h}

According to the problem

K^{'} = \frac{K}{2}

\frac{K}{2 K} = \frac{h ^{'}}{h}

h^{'} = \frac{h}{2} = \frac{5}{2} m = 2 \cdot 5 m

Q. A stone of mass $2 k g$ is projected upward with the kinetic energy of $98 J$ . The height at which the kinetic energy of the stone becomes half of its original value is given by

$5 m$

$2.5 m$

$1.5 m$

$0.5 m$

Q. A stone of mass 2kg is projected upward with the kinetic energy of 98J . The height at which the kinetic energy of the stone becomes half of its original value is given by

5m

2.5m

1.5m

0.5m

Q. A stone of mass $2 k g$ is projected upward with the kinetic energy of $98 J$ . The height at which the kinetic energy of the stone becomes half of its original value is given by

$5 m$

$2.5 m$

$1.5 m$

$0.5 m$