A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v0 as shown in figure. If the string gets slack at some point P making an angle θ from the horizontal, the ratio of the speed v of the bob at point P to its initial speed v0 is : 
Held on 30 Apr 2025 · Verified 9 Jul 2026.
(sinθ)21
(2+3sinθ1)21
(2+3sinθcosθ)21
(2+3sinθsinθ)21
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A bullet of mass 10 g moving with 400 m/s penetrates a wall and comes to rest. The loss in kinetic energy is:
Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 $\mathrm{km} / \mathrm{h}$ in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of $60^{\circ}$ with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )
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A balloon is made of a material of surface tension $S$ and its inflation outlet (from where gas is filled in it) has small area $A$. It is filled with a gas of density $\rho$ and takes a spherical shape of radius $R$. When the gas is allowed to flow freely out of it, its radius changes from $R$ to 0 (zero) in time $T$. If the speed $\eta(r)$ of gas coming out of the balloon depends on $r$ as $r^\alpha$ and $T \propto S^\alpha A^\beta \rho^\gamma R^\delta$ then
Work through every NEET UG Mechanics PYQ, year by year.
