Work Energy and Power - Result Question 6
8. A body of mass $3 kg$ is under a constant force which causes a displacement $s$ in metres in it, given by the relation $s=\frac{1}{3} t^{2}$, where $t$ is in seconds. Work done by the force in 2 seconds is
[2006]
(a) $\frac{3}{8} J$
(b) $\frac{8}{3} J$
(c) $\frac{19}{5} J$
(d) $\frac{5}{19} J$
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Answer:
Correct Answer: 8. (b)
Solution:
- (b) Acceleration $=\frac{d^{2} s}{d t^{2}}=\frac{2}{3} m / s^{2}$
Case (b): Suppose the two springs stretched by distance $x_P$ and $x_Q$ by the same force $F$.
$ \text{ Then, } \quad F=k_p x_p^{2}=k_Q x_Q $
Force acting on the body
$=3 \times \frac{2}{3}=2$ newton
Displacement in 2 secs $=\frac{1}{3} \times 2 \times 2=\frac{4}{3} m$
Work done $=2 \times \frac{4}{3}=\frac{8}{3} J$
