Correct Answer - Option 1 : 4.8 N-S
Concept:
Impulse
- When a large force works on a body for a very small time interval, it is called impulsive force.
- An impulsive force does not remain constant, but changes first from zero to maximum and then from maximum to zero. In such case, we measure the total effect of force.
- The impulse caused by a force during a specific time interval is equal to the body's change of momentum during that time interval.
- Impulse, effectively, is a measure of change in momentum.
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Impulse of a force is a measure of the total effect of force.
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Impulse is a vector quantity and its direction is same as that of force.
- SI unit of impulse is Newton-second or kg-m-s-1.
\(\vec I = \mathop \smallint \nolimits_{{t_1}}^{{t_2}} \overrightarrow {F\;} \cdot dt\)
Where, I = impulse, F = force and dt = very small time interval
Hence according to given explanation above
- Impulse, \(I=~\int \frac{dp}{dt}.dt⇒ i.e.,~I=\left( {{p}_{2}}-{{p}_{1}} \right)=\text{ }\!\!Δ\!\!\text{ }p\)
- therefore we can say that impulse is equals to change in momentum
Calculation:
Mass of the ball (m) = 150 g = 0.15 kg
Initial velocity (u) = 12 m/s
Final velocity (v) = 20 m/s
Time = 0.01 s
Initial Momentum p1 = 0.15 × (-12) = -1.8 kg m/s
Final Momentum p2 = 0.15 kg × 20 = 3 kg m/s
Impulse = F × T = change of momentum
⇒ F × T = p2 - p1 = (3 - (-1.8)) = 4.8
⇒ F × 0.01 = 4.8
⇒ F = 480 N -s
