Kinematics

JEE Main level, single correct, medium

79 of 308

Question 79 of 308

If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it
penetrate more before coming to rest?

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Answer: (A) 1 cm

Let the initial velocity of the body be v. Hence the final velocity = v/2
Applying v2=u2−2as⇒(v2)2=v2−2⋅a⋅3⇒a=v2/8v^2=u^2-2 a s \Rightarrow\left(\frac{v}{2}\right)^2=v^2-2 \cdot a \cdot 3 \Rightarrow a=v^2 / 8
In IInd case when the body comes to rest, final velocity = 0, initial velocity = v/2
Again, (0)2=(v2)2−2⋅v28⋅s;(0)^2=\left(\frac{v}{2}\right)^2-2 \cdot \frac{v^2}{8} \cdot s ; or s=1 cms=1 \mathrm{~cm}
So the extra penetration will be 1 cm1 \mathrm{~cm}

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