1.a If a body loses half of its vel...
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1.a If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest? (AIEEE - 2002, 4/3001 (1) 1 cm (2) 2 cm (D) 4 cm no (3) 3 cm

JEE/Engineering Exams
Physics
Solution
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Let the initial velocity of the body be u. Its velocity becomes u/2 after penetrating ( 3 mathrm{cm} ) in the block. We can calculate the deceleration of the body using these. ( v^{2}=u^{2}+2 a s ) ( u^{2} / 4=u^{2}+2 a times 3 ) ( -3 u^{2} / 4=6 a ) ( a=-u^{2} / 8 ) Now, we can calculate the distance the body travels till it comes to rest. ( v^{2}=u^{2}+2 a s ) ( 0=u^{2}+2 timesleft(-u^{2} / 8right) times s ) ( u^{2}=u^{2} s / 4 ) ( mathrm{s}=4 mathrm{cm} ) Therefore, the body penetrates ( 1 mathrm{cm} ) ( (4-3=1 mathrm{cm}) ) more before coming to rest.
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