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Force required to bring a body of mass m moving on a straight line from speed u to speed v is given as _____.
1. \(\frac{v-u}{t}\)
2. \(m\frac{v-u}{t}\)
3. \(m\frac{v^2-u^2}{t}\)
4. mt (v - u)

1 Answer

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Correct Answer - Option 2 : \(m\frac{v-u}{t}\)

Concept:

Momentum

The force multiplied by velocity gives momentum. 

It is having unit Newton second or kg m s - 1.

Second Law of Motion

The rate of change of momentum is directly proportional to the external unbalanced force. 

\(F \propto \frac{Δ p}{Δ t}\)

Δp is the change in momentum in time Δt.

Experimentally

\(F = \frac{Δ p}{Δ t}\)

Calculation:

Given, initial speed u, final speed v, mass m 

Then Change in momentum Δp = mv - mu

So, we can say

\(F = \frac{mv - mu}{Δ t} = m \frac{v-u}{t}\)

So the correct option is \(m\frac{v-u}{t}\)

1. Newton’s first law of motion

It states that every object will remain in uniform motion in a straight line unless forced to change its state by the action of an external force.

It gives the basics idea of force.

2. Newton’s second law of motion

It states that force applied is equal to change in momentum per unit change in time.

Force (F) = Mass (m) × Acceleration (a)

It gives the formula and final definition of the force.

3. Newton’s third law of motion

It states that for every action, there is an equal and opposite reaction.

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