Correct Answer - Option 4 : 25 Ns
CONCEPT:
Impulse:
- A large force acting for a short time to produce a finite change in momentum is called impulse.
- The product of force and time is called an impulse of force.
\(\Rightarrow I=FΔ t\)
Where I = impulse, F = applied force and Δt = time
Newton's second law of motion:
- According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the applied unbalanced force.
- The magnitude of the force is given as,
\(\Rightarrow F=\frac{Δ P}{Δ t}\)
Where ΔP = change in momentum
CALCULATION:
Given m = 2.5 kg, u = 0 m/s and v = 10 m/s
Where m = mass, u = initial velocity and v = final velocity
\(\Rightarrow I=FΔ t\) -----(1)
- By Newton's second law of motion,
\(\Rightarrow F=\frac{Δ P}{Δ t}\) -----(2)
By equation 1 and equation 2,
\(\Rightarrow I=\frac{Δ P}{Δ t}\times\Delta t\)
\(\Rightarrow I=Δ P\) -----(3)
- The change in momentum is given as,
\(\Rightarrow Δ P=m(v-u)\)
\(\Rightarrow Δ P=2.5(10-0)\)
\(\Rightarrow Δ P=25\,Ns\) -----(4)
By equation 3 and equation 4,
\(\Rightarrow I=25 \,Ns\)
Hence, option 4 is correct.
