Question

A body is thrown up with a kinetic energy of 10 joules. If it attains a maximum height of 5 meter. Find the mass of the body

Answer 1

Question :-

A body is thrown up with a kinetic energy of 10 joules. If it attains a maximum height of 5 meter. Find the mass of the body .

Answer :-

Given :

Kinetic energy = 10 J

Height = 5 m

We know that :

Kinetic energy = potential energy at that height .

==> m g h = 10 J

==> m × 10 m/s² × 5 m = 10 J

==> m × 50 m²/s² = 10 kg m²/s²

==> m = 10 / 50 kg

==> m = 1/5 kg

==> m = 0.2 kg

==> m = 200 g

The mass of the body is 200 g

Answer 2

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Given,
A body is thrown upwards.
Kinetic Energy of the body $KE = 10\: J$
Maximum height attained by the body $h= 5\: mts$

$\underline{\large{\textbf{Step-1}}}$
Find the Initial velocity of the body.

Using the formula,
$v^{2}-u^{2}=2as$

Here, in this case,
For a body thrown upwards v = 0
Distance travelled by the body s=h = 5 mts
Acceleration a = -g = -9.8 m/s
(Since, the body is travelling opposite to direction of gravity)

Substituting Values

$\implies 0-u^{2} = 2\times(-9.8)\times5$

$\implies u^{2} = 98$

$\implies u= 9.9\: m/s$

So, Initial velocity of the body = 9.9 m/s

$\underline{\large{\textbf{Step-2}}}$
Find the Mass of the body

Using the relation,
$KE = \frac{1}{2}\,mv^{2}$

Here,
velocity v = u
Given , KE = 10 J

Substituting Values ,

$KE = \frac{1}{2}\,mu^{2}$

$\implies 10= \frac{1}{2}\,m(9.9)^{2}$

$\implies 20= m(98.01)$

$\implies m = \frac{20}{98.01}$

$\implies m = 0.204\: kg$

Therefore,
Mass of the body = 0.204 kg = 204 gms

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