Q.

In the arrangement shown, the block is released from rest from  x = 0 (when the spring was in its natural length), on an incline having µ = 0.5x. The maximum elongation in the spring will be (in m) use g=10m/s2

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answer is 2.

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Detailed Solution

Wg+Wf+WN+Wspring=ΔK ⇒(50sin37o)xm−∫0xm(0.5x)(50cos37o)dx+0−12kxm2=12m(vf2−vi2)At the point of max. elongation v = 0​⇒30xm−10xm2−5xm2=0⇒30=10xm+5xm⇒15xm=30​⇒xm=2m
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