IIT JEE , AIEEE Forum - Physics , Mechanics - Good Questions from Work Energy Power..Try them

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Q.1
A ring of mass m slides on a smooth vertical rod. Attached to the ring is a light string passing over a smooth peg at a distance b from the rod, and at the other end of string is a mass M (>m). The ring is held on a level with the peg and released.
Show that it first comes to rest after falling a distance :
(2mMa)/ (M²- m²)...
See Fig.1

Q.2
A small body A starts sliding from the height h down an inclined groove passing into a half-circle of radius h/2. Assuming the friction to be negligible, find the velocity of the body at the highest point of its trajectory( after breaking off the groove.)
Ans = (2/3)*

(gh/3)
See Fig.2

Q.3
A particle is projected along the inside of a smooth fixed sphere, from the lowest point, with a velocity equal to that due to falling freely down the vertical diameter of the sphere. Show that the particle will leave the sphere and afterwards pass vertically over the point of projection at a distance equal to 25/32 of the diameter.

Q.4
A thin rim of mass m and radius r rolls down an inclined plane of slope

, winding thereby a ribbon of linear density

. At the initial moment, the rim is at a height h above the horizontal surface.
Determine the distance S from the foot of the inclined plane at which the rim stops, assuming that the incline plane smoothly changes into the horizontal plane.
Ans : S = (mg +

(hcosec

)(r - h/2) /

r
See Fig. 3

Q.5
A chain AB of length L is loaded in a smooth horizontal tube so that its fraction of length h hangs freely and touches the surface of the table with its end B. At a certain moment, the end A of the chain is set free. With what velocity will this end of the chain slip out of the tube.
Ans :

(2gh log_e(l/h))
See Fig. 4

Q.6
A body of mass m was slowly hauled up the hill by a force E which at each point was directed along a tangent to the trajectory. Find the work performed by this force, if the height of the hill is h, the length of its base l and coefficient of kinetic fraction k.
Ans : mg (h+ kl)
See Fig.5

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