Question

A body of mass 12kg is moving with a velocity of 4 m/s.then find the linear momentum of body


with step by step process​

Answer 1

The linear momentum of the body is 48 kgm/s.

Explanation

In the question, it's been stated that a body of mass 12kg is moving with a velocity of 4 m/s. We've been asked to calculate the linear momentum of the body.

Well, a body is to possess linear momentum, if it is moving along a straight path and it is given by the product of mass and velocity.

$\qquad \: \: \: \boxed{\sf{Momentum = Mass*Velocity}}$

The S.I. unit of momentum is kgm/s. Since the S.I. units of mass and velocity are 'kg' and 'm/s', respectively, when they are multiplied, it's written as kgm/s.

Now, by using this formula, the linear momentum of the body can be determined.

• Momentum (p) = ?
• Mass (m) = 12 kg
• Velocity (v) = 4 m/s

Substituting the values in the formula:

$\twoheadrightarrow \quad\sf{p = mv}$

$\twoheadrightarrow \quad\sf{p = 12 \times 4}$

$\twoheadrightarrow \quad \boxed{ \bf \red{p = 48\: kgm {s}^{ - 1} }}$

∴ The linear momentum of the body is 48 kgm/s.

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Additionally, let's know how the dimensional formula of linear momentum is derived.

We know that the general formula of linear momentum is given by:

$\twoheadrightarrow\quad\sf{Mass*Velocity}$

where, the dimensional formulae of:

• Mass (m) = $\sf{[M^{1}\:L^{0}\:T^{0}]}$
• Velocity (v) = $\sf{[M^{0}\:L^{1}\:T^{-1}]}$

Now, substituting these values in the general formula:

$\twoheadrightarrow \quad\sf{p = mv}$

$\twoheadrightarrow \quad\sf{p = [M^{1}\:L^{0}\:T^{0}] *[M^{0}\:L^{1}\:T^{-1}] }$

$\twoheadrightarrow \quad\sf{p = [M^{1}\:L^{1}\:T^{-1}]}$

$\sf{\therefore\: Momentum = [MLT^{-1}]}$