Q: The workdone to accelerate a body from 30 m/s to 60 m/s is three times the work done to accelerate it from 10 m/s to ‘ v ‘ . The value of ‘ v ‘ in m/s is

(a) 30

(b) 20√2

(c) 30√3

(d) 10√10

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Ans: (d)

Sol: $ \displaystyle \frac{1}{2} m (60^2 – 30^2) = 3 \times \frac{1}{2} m (v^2 – 10^2)$

3600 – 900 = 3 (v^{2} – 100 )

2700 = 3 (v^{2} – 100 )

900 = (v^{2} – 100 )

v^{2} = 1000

$ \displaystyle v = \sqrt{1000} = 10 \sqrt{10} $