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Question: What is the velocity of a body of mass \( 100g \) having KE of \( 20J \) ? \( \left( A \right)\,2...

What is the velocity of a body of mass 100g100g having KE of 20J20J ?
(A) 2ms−1\left( A \right)\,2m{s^{ - 1}}
(B)20ms−1\left( B \right)20m{s^{ - 1}}
(C) 40ms−1\left( C \right)\,40m{s^{ - 1}}
(D) None  of  these\left( D \right)\,None\,\,of\,\,these

Explanation

Solution

Learn the Kinetic Energy formula. Kinetic Energy is the energy possessed by a body due to its motion. In classical mechanics, kinetic energy is equal to half an object’s mass multiplied by the velocity square. Applying this we can find the value of velocity.
KE=12mv2KE = \dfrac{1}{2}m{v^2}
Where,
KE= Kinetic Energy,
m= Mass of the body,
v= Velocity of the body.

Complete answer:
We use Joules, kilogram and meter per second as our default SI units.
According to the given problem,
Kinetic energy of a body is given that is 20J20J .
As we know the SI unit of energy the same SI unit is also applicable to kinetic energy that is Joule.
Mass of the body is given that is 100g100g .
But the SI unit of mass is Kg.
So first we have to convert gram into kilogram.
We know that,
1g=10−3Kg1g = {10^{ - 3}}Kg
Now for 100g100g we can write,
100g=100×10−3Kg100g = 100 \times {10^{ - 3}}Kg
⇒100g=10−1Kg\Rightarrow 100g = {10^{ - 1}}Kg
Hence the mass of the body is 10−1Kg{10^{ - 1}}Kg .
Now putting these values in kinetic energy formula we will get,
KE=12mv2KE = \dfrac{1}{2}m{v^2}
By rearranging the above equation we get,
v2=2KEm{v^2} = \dfrac{{2KE}}{m}
Taking square other side we get,
v=2KEmv = \sqrt {\dfrac{{2KE}}{m}}
Now putting the respective values
v=2×20J10−1Kgv = \sqrt {\dfrac{{2 \times 20J}}{{{{10}^{ - 1}}Kg}}}
⇒v=40J10−1Kg\Rightarrow v = \sqrt {\dfrac{{40J}}{{{{10}^{ - 1}}Kg}}}
⇒v=400J Kg−1\Rightarrow v = \sqrt {400J\,K{g^{ - 1}}}
⇒v=20ms−1\Rightarrow {v = 20m{s^{ - 1}}}
Hence 20ms−120m{s^{ - 1}} is the velocity of a body of mass 100g100g having KE of 20J20J .
Therefore the correct option is (B)\left( B \right) .

Note:
Before finding the velocity first check that the given values are in their proper SI unit or not. If not then first convert them into their default SI units. As in this problem, the mass of the body is not in its SI unit. If you are not converting it into kilograms then you will note get the correct answer.