CLASS XI - PHYSICS

✤ General instructions:

  1. The Question Paper contains five sections.

  2. Section A has 10 questions carry 1 mark each.

  3. Section B has 4 questions carry 2 marks each.

  4. Section C has 4 questions carry 3 marks each.

  5. Section D has 1 question of 5 marks.

  6. Section E has 1 question of 5 marks

✤ SECTION A

1. A person is standing in an elevator. In which situation he finds his weight

 less?

    (a) When the elevator moves upward with constant acceleration

    (b) When the elevator moves downward with constant acceleration

    (c) When the elevator moves upward with uniform velocity

    (d) When the elevator moves downward with uniform velocity

2. What is the minimum velocity with which a body of mass m must enter

 a vertical loop of radius R so that it can complete the loop?

     (a) √(gR) (b) √(2gR) (c) √(3gR) (d) √(5gR)

3. The force on a particle as the function of displacement x (in x-direction)

 is given by F=10+0.5 x. The work done corresponding to displacement

 of particle from x=0 to x=2 unit is:

   (a) 25 J (b) 29 J (c) 21 J (d) 18 J

4. If the kinetic energy of a body becomes four times of its initial value, then

 New momentum will:

      (a) become twice its initial value

      (b) become thrice its initial value

      (c) become four times its initial value

      (d) remain constant

5. The angular momentum of a moving body remains constant, if:

      (a) net external force is applied

      (b) net pressure is applied

      (c) net external torque is applied

      (d) net external torque is not applied

6. Two particles which are initially at rest move towards each other under

 the action of their internal attraction. If their speeds are V and 2V at any

 instant, then the speed of center of mass of the system will be

      (a) 2V (b) zero (c) 1.5V (d) V

7. A satellite of the earth is revolving in a circular orbit with a uniform speed

 V. If the gravitational force suddenly disappears, the satellite will:

      (a) continue to move with velocity V along the original orbit

      (b) move with a velocity V tangentially to the original orbit

      (c) fall down with increasing velocity

      (d) ultimately come to rest, somewhere on the original orbit

8. Two satellites of masses m₁ and m₂ (m₁ > m₂) are going around the earth

 in orbits of radii r₁ and r₂ (r₁ > r₂). Which statement about their

 velocities is correct?

      (a) v₁ = v₂ (b) v₁ < v₂

   (c) v₁ > v₂ (d) v₁ ∝ v₂

ASSERTIONS AND REASONS

Directions. In the following questions, a statement of assertion is followed by a statement of reason. Mark the correct choice as

    (a) If both assertion and reason are true and reason is the correct explanation of

   the assertion,

    (b) If both assertion and reason are true but reason is not correct explanation of

   the assertion,

    (c) If assertion is true, but reason is false.

    (d) If both assertion and reason are false.

9. Assertion. It is difficult to move a cycle along the road with its brakes

       on.

     Reason. Sliding friction is greater than rolling friction.

10. Assertion. When a body moves along a circular path, no work is done

       by the centripetal force.

     Reason. The centripetal force is used in moving the body along the

       circular path and hence no work is done.

✤ SECTION-B

11. Obtain an expression for the maximum speed with which a vehicle can

  safely negotiate a curved road banked at an angle θ. The coefficient of

  friction between the wheels and the road is μ.

12. Two springs have force constants k₁ & k₂ (k₁> k₂). On which spring is

  more work done, if

      (i) they are stretched by the same force and

      (ii) they are stretched by the same amount?

13. From a uniform circular disc of radius R, a circular hole of radius R/2

  is cut out. The centre of the hole is at R/2 from the centre of original

  disc. Locate the centre of gravity of the resulting body.

OR

     The angular speed of a motor wheel is increased from 1200 rpm to

  3120 rpm in 16 seconds.

       (i) What is its angular acceleration, assuming the acceleration to

     be uniform?

       (ii) How many revolutions does the wheel make during this time?

14. Define acceleration due to gravity. Derive expression for the variation

  of ‘g’ with height from the surface of the earth.

✤ SECTION-C

15. Prove that the angular momentum of a particle is equal to twice the

  product of its mass and areal velocity. How does it lead to Kepler's

  second law of planetary motion?

16. (i) What will be the duration of the day, if earth suddenly shrinks to

    1/64 of its original volume, mass remaining the same?

  (ii) Why are the doors provided with handles near the outer edges far

    away from the hinges?

OR

   (i) Energy of 484 J is spent in increasing the speed of a flywheel from

      60 rpm to 360 rpm. Find the moment of inertia of the wheel.

   (ii) Does the moment of inertia of a rigid body change with the speed

       of rotation?

17. Derive an expression for the escape velocity of a satellite projected

  from the surface of the earth.

18. Find the potential energy of a system of four particles, each of mass m,

  placed at the vertices of a square of side L. Also obtain the potential at

  the centre of the square.

✤ SECTION-D

19. (i) Define elastic collision. Two bodies of masses m₁ and m2 moving

   with velocities u₁ and u2 undergo one dimensional elastic collision.

   Determine their velocities after the collision.

 (ii) What percentage of kinetic energy of a moving particle is transferred

   to a stationary particle, when moving particle strikes with a

   stationary particle of mass 9 times in mass?

OR

 (i) Derive an expression for the potential energy of an elastic stretched

   spring. Also plot graph between energy and displacement to show

   conservation of energy in elastic spring.

 (ii) A ball at rest is dropped from a height of 12 m. It loses 25% of its

   kinetic energy in striking the ground, find the height to which it

   bounces. How do you account for the loss in kinetic energy?

✤ SECTION-E

20. Conservation of Linear Momentum

  Consider an isolated system of n interacting particles. The mutual forces between pairs of particles in the system cause changes in momenta of the individual particles. By third lose, the mutual forces between any pair of particles are equal and opposite. By second b/w, the changes in momenta for any pair of particles are Fit and -FAt. Thus the momentum

  changes cancel in pairs and total momentum of the system remains constant. That leads to a fundamental principle of physics called the law of conservation of linear momentum. This law states that the total linear momentum of an isolated system of interacting particles is conserved. The recoil of a gun on firing, explosion of a bomb into different fragments due to internal forces, the working of rockets and jet planes, etc; can the explained on basis of momentum conservation

QUESTIONS (Answer the following questions)

 (i) A gun fires a bullet of mass 50 g with a velocity of 30 m/s. Because

   of this, the gun is pushed back with a velocity of 1 m/s. The mass of

   the gun is:

    (a) 5.5 kg (b) 3.5 kg (c) 1.5 kg (d) 0.5 kg

 (ii) A body of mass M moving with velocity V explodes into two equal

   parts. If one comes to rest and the other part moves with velocity v,

   what would be the value of v?

    (a) V (b) V/2 (c) 4V (d) 2 V

 (iii) Draw a graph between momentum and mass for constant speed.

OR

    Why a cricket player lowers his hands while catching a ball?

 (iv) A rubber ball of mass 50g falls from a height of 1m and rebounds to

   a height of 0.5m. Find the impulse and the average force between the

   ball and ground if the time for which they are in contact was 0.1s.

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