The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is

A vertical frictionless semicircular track of radius R is fixed on the edge ofmovable trolley. Initially the system is at rest and a mass m is kept at the top of the track. The trolley starts moving to the right with a uniform horizontal acceleration . The mass slides down the track, eventually losing contact with it and dropping to the floor h below the trolley The time taken by the mass to drop on the floor, after losing contact is

A vertical frictionless semicircular track of radius R is fixed on the edge ofmovable trolley. Initially the system is at rest and a mass m is kept at the top of the track. The trolley starts moving to the right with a uniform horizontal acceleration . The mass slides down the track, eventually losing contact with it and dropping to the floor h below the trolley The height at which mass m losing contact is

The final product (IV) in the sequence of reactions
 is

graph for a particle is as shown. The distance travelled in the first is

A vertical frictionless semicircular track of radius R is fixed on the edge ofmovable trolley. Initially the system is at rest and a mass m is kept at the top of the track. The trolley starts moving to the right with a uniform horizontal acceleration . The mass slides down the track, eventually losing contact with it and dropping to the floor h below the trolley The angle with vertical, at which it losses contact with the trolley is

Ram and Shyam are two fast friends since childhood. Shyam neglected studies and now has no means to earn money other than a camel whereas Ram becomes an engineer. Now both are working in the same factory. Shyam uses camel to transport the load within the factory.

Due to low salary & degradation in health of camel, Shyam becomes worried and meet his friend Ram and discusses his problem. Ram collected some data & with some assumptions concluded the following: The load used in each trip is 1000 kg and has friction coefficient = 0.1 and = 0.2. Mass of camel is 500 kg. Load is accelerated for first 50 m with constant acceleration, then it is pulled at a constant speed of 5m/s for 2 km and at last stopped with constant retardation in 50 m. From biological data, the rate of consumption of energy of camel can be expressed as where P is the power and v is the velocity of the camel. After calculations on different issues Ram suggested proper food, speed of camel etc. to his friend. For the welfare of Shyam, Ram wrote a letter to the management to increase his salary.The total energy consumed of the camel during the trip of 2100 m is–

Ram and Shyam are two fast friends since childhood. Shyam neglected studies and now has no means to earn money other than a camel whereas Ram becomes an engineer. Now both are working in the same factory. Shyam uses camel to transport the load within the factory.

Due to low salary & degradation in health of camel, Shyam becomes worried and meet his friend Ram and discusses his problem. Ram collected some data & with some assumptions concluded the following: The load used in each trip is 1000 kg and has friction coefficient = 0.1 and = 0.2. Mass of camel is 500 kg. Load is accelerated for first 50 m with constant acceleration, then it is pulled at a constant speed of 5 for 2 km and at last stopped with constant retardation in 50 m. From biological data, the rate of consumption of energy of camel can be expressed as where P is the power and v is the velocity of the camel. After calculations on different issues Ram suggested proper food, speed of camel etc. to his friend. For the welfare of Shyam, Ram wrote a letter to the management to increase his salary.The ratio of the energy consumed of the camel during uniform motion for the two cases when it moves with speed 5 m/s to the case when it moves with 10 m/s.

A man wants to reach point on the opposite bank of a river flowing at a speed as shown in figure. What minimum speed relative to water should the man have so that he can reach point ? In which direction should be swim?

Which one of the following will most readily be dehydrated in acidic conditions?

Which of the following will not react with 

A particle starts from rest at and moves in a straight line with acceleration as shown in figure. The velocity of the particle at is

A frictionless wire is fixed on a sphere of radius . A very small spherical ball slips on this wire. The time taken by this ball to slip from to is

For the velocity-time graph shown in figure below the distance covered by the body in last two seconds of its motion is what fraction of the total distance covered by it in all the seven seconds

The diagram shows the mass of some parcels on weighing machine.

Find the value of y.

Hence y=1

Esterification of alcohols involves: