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Q.

A block of 4 kg mass starts at rest and slides a distance d down a frictionless incline (angle 30^o) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is 400 N/m. The value of d is (take g = 10 ms^-2)

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a

25 cm

b

62.5 cm

c

None of the above

d

37.5 cm

answer is B.

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Detailed Solution

$\begin{array}{l} W_{gravity} = {ΔU}_{spring} \\ mgsin θ (d + 0 .25) = \frac{1}{2} k (0 .25)^{2} \end{array}$

which gives d = 37.5 cm

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A block of 4 kg mass starts at rest and slides a distance d down a frictionless incline (angle 30o) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is 400 N/m. The value of d is (take g = 10 ms-2)