A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x = 3t –4t2+ t3, where x is in metres and t is in seconds. The work done during the first 4 seconds is
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Solution
A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together,the loss in kinetic energy due to collision is
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Solution
A particle of mass 10 kg moving eastwards with a speed 5ms-1 collides with another particle of the same mass moving north-wards with the same speed 5ms-1. The two particles coalesce on collision. The new particle of mass 20 kg will move in the north-east direction with velocity
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Solution
A particle moves in the X–Y plane under the influence of a force Fr such that its instantaneous momentum is
\(\overrightarrow{p}=\overrightarrow{i}2cos\, t+\overrightarrow{j}2sin\, t\).What is the angle between the force and instantaneous momentum ?
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Solution
The ball rolls down without slipping (which is at rest at a)along ab having friction. It rolls to a maximum height hc where bc has no friction. Ka, Kb and Kc are kinetic energies at a, b and c.
Which of the following is correct ?
A horse drinks water from a cubical container of side 1 m.The level of the stomach of horse is at 2 m from the ground.Assume that all the water drunk by the horse is at a level of 2m from the ground. Then minimum work done by the horse in drinking the entire water of the container is(Take ρwater= 1000kg/m3 and g= 10 m/s2 ) –
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Solution
The mass of water ism = 1 × 103 kg
∴ The increase in potential energy of water is
= mgh = (1× 103) (10) (1.5) = 15 kJ