Question

A moving body of mass 500 gram has 100 J of kinetic energy. Calculate the speed of the body​

Answer 1

Given :

• Mass of the body = 500 g

• Kinetic energy = 100 J

To find :

The velocity of the body.

Solution :

First let us convert the mass of the body in kg from g.

To find the mass in the kg , we have to divide the mass (in g) by 1000 i.e,

• m = 500 g

==> m = (500/1000) kg

==> m = ½ kg

==> m = 0.5 kg

Hence, the mass of the body in kg is 0.5 kg.

Let the velocity of the body be v m/s.

We know the formula for Kinetic energy of a body i.e,

$\boxed{\bf{KE = \dfrac{1}{2}mv^{2}}}$

Where :

• K·E = Kinetic energy possessed by the body
• m = Mass of the body.
• v = Velocity of the body.

Now , using the above formula and substituting the values in it, we get :

$:\implies \bf{KE = \dfrac{1}{2}mv^{2}}$

$:\implies \bf{100 = \dfrac{1}{2} \times 0.5 \times v^{2}}$

$:\implies \bf{100 = \dfrac{1}{2} \times \dfrac{5}{10} \times v^{2}}$

$:\implies \bf{100 = \dfrac{1}{2} \times \dfrac{1}{2} \times v^{2}}$

$:\implies \bf{100 = \dfrac{1}{2 \times 2} \times v^{2}}$

$:\implies \bf{100 = \dfrac{1}{4} \times v^{2}}$

$:\implies \bf{100 \times 4 = v^{2}}$

$:\implies \bf{400 = v^{2}}$

$:\implies \bf{\sqrt{400} = v}$

$:\implies \bf{20 = v}$

$\boxed{\therefore \bf{Velocity\:(v) = 20\:ms^{-1}}}$

Hence, the velocity of the body is 20 m/s

Answer 2

$\Large \dag\underline{\underline{ \green{\sf Given:}}}\dag$

✥ Mass of body, m = 500g

✥ Kinetic Energy, K = 100J

$\Large \dag\underline{\underline{ \green{\sf Find:}}}\dag$

✣ What is the speed of the Body

$\Large \dag\underline{\underline{ \green{\sf Solution:}}}\dag$

we, know that

➛ $\boxed{\red{\sf K = \dfrac{1}{2} m {v}^{2}}}$

where,

• Mass, m = 500g

=> 1kg = 1000g

=> 500g = 500/1000 = 1/2 g

• Kinetic Energy, K = 100J

So,

➟ $\red{\sf K = \dfrac{1}{2} m {v}^{2}}$

➟ $\red{\sf 100 = \dfrac{1}{2} \times \dfrac{1}{2} {v}^{2}}$

➟ $\red{\sf 100 = \dfrac{1}{4} {v}^{2}}$

➟ $\red{\sf 100 \times \dfrac{4}{1} = {v}^{2}}$

➟ $\red{\sf 400 = {v}^{2}}$

➟ $\red{\sf \sqrt{400} = v}$

➟ $\red{\sf 20 = v}$

➟ $\red{\sf v = 20m/s}$

Hence, Speed of the object is 20m/s