A smooth block of mass 10kg is released from rest from a height 5m. It slides and compresses the spring of stiffness as shown in figure 200Nm. The maximum compression of the spring is
A
2√5m
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B
√5m
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C
√2.5m
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D
0
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Solution
The correct option is B√5m Using law of conservation of energy. ΔK=−ΔU
Since, block starts from rest and the block will come to rest at the time of maximum Compression ΔK=0. ⇒ΔU=0
Taking spring and block as one system ΔU=(ΔU)spring+(ΔU)gravity=0. (ΔU)spring=−(ΔU)gravity 12kx2−0=−(0−mgh)⇒12kx2=mgh
Then x=√2mghk=√2×10×10×5200=√5m