Questions
A light and thin rod of length l is lying on smooth horizontal table. Two small balls of masses 3m and m are fixed on two ends of a massless rod. The rod is free to rotate about fixed vertical axel passing through midpoint of rod. A third ball of mass 2m is fastened to ball of mass m through a string of length l as shown in figure. The ball is projected horizontally with speed v as shown. The angular velocity of rod, just after the string becomes taut is
detailed solution
Correct option is A
Angular momentum of the rod just before the string become taut is zero. Let us assume the angular velocity of rod just after the string become taut is ω. Impulse imparted by string is J.sinθ=4l5×l=45⇒θ=53∘Using concept of Angular Impulse,Jcos53∘l2=m+3ml24ω⇒3J5=2mlω⇒J=103mlω−−−−1For 2m mass apply concept of Linear impulse,J=2mvcos530−v1−−−2Using string constraint , v1=ωl2cos53∘=ωl2×35=ω3l10−−−3from 1& 2 So 103mlω=2m3v5−3ωl10∵from3⇒5lω3=3v5−3ωl10⇒5ωl3+3ωl10=3v5⇒50ωl+9ωl30=3v5⇒ω=18v59lTalk to our academic expert!
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A uniform rod is falling without rotation on a smooth horizontal plane. Assuming the collision to be perfectly elastic, the angular velocity of the rod after striking the table is maximum when the rod makes an angle with the horizontal just before striking where is not readable. Find .
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