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Question:

Two similar spring P and Q have spring constantsKPandKQ, such thatKP>KQ. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springWPandWQare related as, in case (a) and case (b), respectively:WP>WQ;WQ>WPWP<WQ;WQ<WPWP=WQ;WP>WQWP=WQ;WP=WQTwo similar spring P and Q have spring constantsKPandKQ, such thatKP>KQ. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springWPandWQare related as, in case (a) and case (b), respectively:WP>WQ;WQ>WPWP<WQ;WQ<WPWP=WQ;WP>WQWP=WQ;WP=WQKPKPKPKPKKKPPPKQKQKQKQKKKQQQKP>KQKP>KQKP>KQKPKKKPPP>>KQKKKQQQWPWPWPWPWWWPPPWQWQWQWQWWWQQQWP>WQ;WQ>WPWP>WQ;WQ>WPWP>WQ;WQ>WPWP>WQ;WQ>WPWPWWWPPP>>WQWWWQQQ;;WQWWWQQQ>>WPWWWPPPWP<WQ;WQ<WPWP<WQ;WQ<WPWP<WQ;WQ<WPWP<WQ;WQ<WPWPWWWPPP<<WQWWWQQQ;;WQWWWQQQ<<WPWWWPPPWP=WQ;WP>WQWP=WQ;WP>WQWP=WQ;WP>WQWP=WQ;WP>WQWPWWWPPP==WQWWWQQQ;;WPWWWPPP>>WQWWWQQQWP=WQ;WP=WQWP=WQ;WP=WQWP=WQ;WP=WQWP=WQ;WP=WQWPWWWPPP==WQWWWQQQ;;WPWWWPPP==WQWWWQQQAWP=WQ;WP=WQWP=WQ;WP=WQWP=WQ;WP=WQWP=WQ;WP=WQWP=WQ;WP=WQWPWWWPPP==WQWWWQQQ;;WPWWWPPP==WQWWWQQQBWP<WQ;WQ<WPWP<WQ;WQ<WPWP<WQ;WQ<WPWP<WQ;WQ<WPWP<WQ;WQ<WPWPWWWPPP<<WQWWWQQQ;;WQWWWQQQ<WQ;WQ>WPWP>WQ;WQ>WPWP>WQ;WQ>WPWP>WQ;WQ>WPWP>WQ;WQ>WPWPWWWPPP>>WQWWWQQQ;;WQWWWQQQ>>WPWWWPPPDWP=WQ;WP>WQWP=WQ;WP>WQWP=WQ;WP>WQWP=WQ;WP>WQWP=WQ;WP>WQWPWWWPPP==WQWWWQQQ;;WPWWWPPP>>WQWWWQQQ?

WP=WQ;WP=WQ

WP<WQ;WQ<WP

WP>WQ;WQ>WP

WP=WQ;WP>WQ

Solution:

Case a) both the springs are stretched by same amount, energy stored springs in P and Q will beWP=12KPΔx2andWQ=12KQΔx2.. (i)givenKP>KQ⇒WP>WQ.. (ii)Case b) both the springs are stretched by same force, energy stored springs in P and Q will beWP=12KPΔx2PandWQ=12KQΔx2Q.. (iii)givenKP>KQ⇒ΔxP<ΔxQ.. (iv)andF=KPΔxP=KQΔxQ.. (v)WP=12KPΔxPΔxPandWQ=12KQΔxQΔxQ.. (vi)from equation (v) substitutingF=KPΔxP=KQΔxQin equation (vi)WP=12FxPandWQ=12FxQgivenΔxP>ΔxQ⇒WP<WQ.. (vii)hence, correct answer is option A.