WBJEE · Physics · Work Power Energy
The kinetic energy \(\left(\mathrm{E}_{\mathrm{k}}\right)\) of a particle moving along \(X\)-axis varies with its position \((X)\) as shown in the figure. The force acting on the particle at \(X=10 \mathrm{~m}\) is
- A \(5 \hat{\mathrm{i} N}\)
- B \(0 \mathrm{~N}\)
- C \(97.5 \hat{\mathrm{i} N}\)
- D \(-5 \hat{\mathrm{i} N}\)
Answer & Solution
Correct Answer
(D) \(-5 \hat{\mathrm{i} N}\)
Step-by-step Solution
Detailed explanation
\[ \frac{d k}{d x}=\frac{d\left(\frac{1}{2} m v^2\right)}{d x}=\frac{1}{2} m \not{2} v \frac{d v}{d x}=m a=F \] So, Force is slope at \(x=10 m \quad F=-\frac{20}{4}=-5 \hat{i}\)
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