Law of Conservation of Energy

Q. The potential energy of a spring is (1/2)Kx²(k=Force constant).How did the equation come?

Q.

When two spheres of equal masses undergo glancing elastic collision with one of them at rest, after the collision they will move

1. opposite to one another

2. in the same direction

3. together

4. at right angle to each other

Q. a particle moves from point p (1, 2, 3) to Q(2, 1, 4) under the action of a constant force F=(2i+j+k) N work done by the force is

Q.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Body $‘P’$ having mass $M$ moving with speed ‘$u$’ has head-on collision elastically with another body ‘$Q$’ having mass ‘$m$’ initially at rest. If $m<<M$, body ‘$Q$’ will have a maximum speed equal to ‘$2u$’ after collision.

Reason R: During elastic collision, the momentum and kinetic energy are both conserved.

In the light of the above statements, choose the most appropriate answer from the options given below:

1. A is correct but R is not correct.

2. Both A and R are correct but R is NOT the correct explanation of A

3. A is not correct but R is correct.

4. Both A and R are correct and R is the correct explanation of A.

Q. An object is taken to a height 2R above the surface of earth the increase in potential energy is

Q. the total mechanical energy of an object of mass m projected from surface of earth with escape speed i

Q. A body at rest explodes into two pieces of unequal mass.The parts will move Arbitrarily In the same direction In opposite directions with equal speeds In opposite directions with unequal speeds

Q. A spring of force constant K is first stretched by distance a from its natural length and then further by distance b the work done in stretching the part b is

Q.

Total Energy of the universe is constant?

1. Yes, of course

2. No, it’s conserved but not constant.
3. Only mechanical energy is conserved.
4. Can't say

Q. Ratio of kinetic energy of a particle projected from ground at highest point to point of projection is 1/4. Angle of projection with horizontal is?

Q. When mass m is attached to the spring of force constant k , then the Spring stretches by l lf the mass oscillates with amplitude l , maximum potential energy stored in the spring is A. kl B. 4kl C. 5/2 mgl D. 2mgl

Q. A force of 10 n holds an ideal spring with 20 n/m spring constant in compression. the potential energy stored in the spring is.

Q.

What name is given to the product of mass and velocity of the object?

Q. A billiard ball at rest is struck horizontally one tenth of the diameter below the top. If P be the impulse of the blow find the initial kinetic energy of the ball, the mass of the ball is being M.

Q. 44.the spring constant of two spring are k and k respectively Spring are stretch up to the limit when potential energy of both becomes equal the ratio of applied force( F1 and F2 )on them will be

Q. A ball of mass m falls freely from rest. Whenit has reached a speed v, it strikes a vertical spring. The spring is compressed by distance y before the ball moves upwards again. Assume that all the energy the ball loses becomes elastic potential energy in the spring. What is the average force exerted by the spring during its compression ?

Q. Upward acceleration of a rocket is given by (where v = speed of gas relative to rocket, M = mass of rocket and m = mass of fuel) with respect to gravity, the acceleration of rocket is given by

Q.

A hole is drilled from the surface of earth to its centre. A particle is dropped from rest at the surface of earth. The speed of the particle when it reaches the centre of the earth in terms of its escape velocity on the surface of earth $v_e$ is

1. 

2. 

3. 

4. 

Q. a body of mass m is allowed to fall with the help of string with downward acceleration g/6 to a distance x the work done by the string is

Q. the kinetic energy of a particle at maximum height becomes 1 fourth of initial kinetic energy. then angle of projection will be

Q. for a black body at temperature 727 degrees C, its rate of energy loss is 20 W and temperature of surrounding is 227degrees C.If temperature of black body is changed to 1227 degrees C , then its rate of energy loss will be?

Q. a ball is dropped on to the floor if the coefficient of restituition is 0.5 the percentage loss of energy of the ball on reboinding fromthe floor

Q. 138.The blocks shown in figure have equal masses. The surface of A is smooth but that of B has a friction coefficient of 0.1 with the floor. Block A is moving at a speed of 10m/s towards B which is kept at rest. Find the distance travelled by B if(a)the collision is perfectly elastic and(b) the collision is perfectly inelastic

Q. 12.A BODY IS DROPPED FROM HEIGHT h.WHELOSS IN ITS POTENTIAL ENERGY IS U THEN ITS VELOCITY IS v .THE MASS OF THE BODY IS = a]UxU/2v b]2v/U c]2v/UxU d]2U/vxv

Q. A bob of mass $0.1kg$ hung from the ceiling of a room by a string $2m$ long is set into oscillation. The speed of the bob at its mean position is $1m{s}^{-1}$.What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

Q. A spring of natural length L compressed to length 7L/8 exerts a force F. The work done by the spring restoring itself to natural length is(in terms of F and l)

Q. From a planet of mass $16M$ and radius $4R$, we wish to send an object to its moon of mass $M$ and radius $R$. Distance between centres of planet and moon is $10R$. Minimum speed at which object should be projected from the surface of planet so that it reaches moon is (Assume that the planet and the moon are at rest)

1. $\sqrt{\frac{10GM}{3R}}$
2. $\sqrt{\frac{8GM}{R}}$
3. $\sqrt{\frac{7GM}{3R}}$
4. $\sqrt{\frac{9GM}{2R}}$

Q. 5.In oblique collision WHY linear momentum remains conserved in perpendicular direction of the line joining their center of mass ?

Q.

A body of mass m is thrown at an angle θ to the horizontal with the initial velocity u. Find the mean power developed by gravity over the whole time of motion of the body?

1. 

2. 

3. 

4. Zero

Q.

In which type of collision it is possible that a ball strikes against the floor and returns with double the velocity?

1. Inelastic

2. Perfectly Inelastic

3. It is not possible

4. Perfectly elastic