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CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

CENTRE OF MASS, LINEAR MOMENTUM AND COLLISION

CENTRE OF MASS, IMPULSE AND MOMENTUM

CIRCULAR MOTION

Two blocks of masses 3kg and 6kg respectivley are placed on a smooth horizontal surface. They are connected by a light spring of force constant k=200N/m. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. Find the maximum extension of the spring.

Assertion: Centre of mass of a rigid body always lies inside the body.

Reason: Centre of mass and centre of gravity coincide if gravity is uniform.

A rocket of mass 20kg has 180kg fuel. The exhaust velocity of the fuel is 1.6km/s. Calculate the minimum rate of consumption of fuel so that the rocket may rise from the ground. Also, calculate the ultimate vertical speed gained by the rocket when the rate of consumption of fuel is (g=9.8m/s2)

(i) 2kg/s (ii) 20kg/s

Comprehension # 1

If net force on a system in a particular direction is zero (say in horizontal direction), we can apply: ΣmRxR=ΣmLxL,ΣmRvR=ΣmLvL and ΣmRaR=ΣmLaL

Here R stands for the masses which are moving towards right and L for the masses towards left, x is displacement, v is velocity and a the acceleration (all with respect to ground).

A small block of mass m=1kg is placed over a wedge of mass M=4kg as shown in figure. Mass m is released from rest. All surface are smooth. Origin O is as shown.

Final velocity of the wedge is ……….m/s :-

in the given figure, α=15m/s2 represents the total accleration of a particle moving in the clockwise direction on a circle radius R = 2.5m aat a given of time The speed of the particle is

The net force versus time graph of a rocket is shown in figure The mass of the rocket is 1200kg . Calculate velocity of rocket, 16 seconds after starting from rest. Neglect gravity.

A rocket of mass m_0 has attained a speed equal to its exhaust speed and that time the mass of the rocket is m . Then the ratio m_0/m is (neglect gravity)

A rocket with an initial mass of 1000 kg , is launched vertically upward from rest under gravity. The rocket burns fuel at the rate of 10 kg per second. The burnt matter is ejected vertically downwards with a speed of 2000 m//s relative to the rocket . Find the velocity of the rocket after 1 min of start.

The graph shown the variation of velocity of a rocket with time. Then, the maximum height attained by the rocket is.

A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 6 xx 10^(3) ms^(-1) What thrust is exerted on the rocket ? What will be the velocity of the rocket at the instant its mass is reduced to (1 // 40) of its initial mass ? Take initial velocity of rocket as zero . Neglect gravity .

A relativistic rocket emits a gas jet with non-relativistic velocity u constant relative to the rocket. Find how the velocity v of the rocket depends on its rest mass m if the initial rest mass of the rocket equals to m_0 .

A rocket is projected vertically upwards and its time velocity graph is shown in the figure-1.115. The maximum height attained by the rocket is :

A rocket is fired upwards. Its velocity versus time graph is shown in the figure-1.131. The maximum height reached by the rocket is:

A rocket motor consumes 100 kg of fuel per second, exhausting it with a speed of 5xx10^(3)ms^(-1) . (i) What force is exerted on the rocket ? (ii) What will be the velocity of the rocket at the instant its mass is reduced (1//20) th of its initial mass, its initial velocity being zero. Neglect gravity.

A rocket is launched upward from the earth surface whose velocity time graph shown in figure. Then maximum height attained by the rocket is :-