KCET · Physics · Work Power Energy
A particle of mass 500 g is at rest. It is free to move along a straight line. The power delivered to the particle varies with time according to the following graph
The momentum of the particle at \(t=5 \mathrm{~s}\) is
- A \(2 \sqrt{5} \mathrm{~N}-\mathrm{s}\)
- B \(5 \sqrt{2} \mathrm{~N}-\mathrm{S}\)
- C \(5 \mathrm{~N}-\mathrm{S}\)
- D \(5.5 \mathrm{~N}-\mathrm{s}\)
Answer & Solution
Correct Answer
(C) \(5 \mathrm{~N}-\mathrm{S}\)
Step-by-step Solution
Detailed explanation
Area under \(P\)-t graph is equal to work done (or change in kinetic energy)
\(\therefore \Delta k=\frac{P^2}{2 m}=\) area of region \(O A B C\)
\(\Rightarrow \frac{P^2}{2 m}=\frac{(2+8) 5}{2}\)
\(\Rightarrow \frac{P^2}{2 \times 0.5}=25 \quad[\because m=500 \mathrm{~g}=0.5 \mathrm{~kg}]\)
\(\Rightarrow P^2=25 \Rightarrow P=5 \mathrm{~kg} \mathrm{~ms}^{-1}\)
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