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Question: A stone attains a momentum of \(1kgm{{s}^{-1}}\) when it flies with a velocity of \(2m{{s}^{-1}}\), ...

A stone attains a momentum of 1kgms−11kgm{{s}^{-1}} when it flies with a velocity of 2ms−12m{{s}^{-1}}, then what will be the mass of the stone?
A. 500g500g
B. 2kg2kg
C. 2g2g
D. None

Explanation

Solution

Momentum of a body is a vector quantity and it is defined as the product of the mass and the velocity of the body. Use the definition of momentum and find the mass of the stone by substituting the given values.

Formula used:
P→=mv→\overrightarrow{P}=m\overrightarrow{v}
Where PP is the momentum of a body, mm is the mass of the body and vv is the velocity of the body.

Complete step by step answer:
When a body is in motion, we change that it possesses some momentum. Momentum of a body is defined as the product of the mass and the velocity of the body. When we talk about momentum of a body, we are concerned with its direction. Its direction is along the direction of the velocity of the body. Therefore, momentum is a vector quantity. If a body of mass m is moving with a velocity v→\overrightarrow{v}, then its momentum is equal to, P→=mv→\overrightarrow{P}=m\overrightarrow{v}. The magnitude of the momentum is equal to P=mvP=mv …. (i).
Since momentum is a product of the mass and velocity, its unit is the product of units of mass and the velocity. Therefore, the unit of momentum is kgms−1kgm{{s}^{-1}}.
It is given that the momentum of the stone is 1kgms−11kg m{{s}^{-1}} and its velocity is 2ms−12m{{s}^{-1}}. This means that P=1kgms−1P=1kgm{{s}^{-1}}and v=2ms−1v=2m{{s}^{-1}}.
Substitute the values of P and v in equation (i).
1=m(2)1=m(2)
⇒m=0.5kg ∴m=500g\Rightarrow m=0.5kg\\\ \therefore m = 500g
This means that the mass of the stone is equal to 500 g.

Hence, the correct option is A.

Note: Momentum is the quantity of motion and is compounded of the quantity of the matter moved, and the velocity with which it moves. Momentum is present when you walk, run, etc. Also if a bicycle and a car travel down the street at the equal velocity the car will have the most momentum.Since velocity is considered to be a vector, momentum is considered a vector as well. This means momentum has a significance of momentum and also has a direction. The momentum direction indicated by a vector or an arrow.