Mechanics Test-1Time: 1 hr Marks: 100

More than one options may be correct. Marking scheme: +4 (R), -2 (W), 0 (N)

1. The pair of physical quantities that have the same dimensions are:a. Reynolds number and coefficient of frictionb. Curie and frequency of light wave

c. Latent heat and gravitational potentiald. Planck’s constant and torque

2. A block of mass 5 kg is kept on a rough horizontal surface with = 0.4. When a force of 20 N is applied at angle 30o, then (f = frictional force):a. f = 16 Nb. f = 17.3 N

c. a = 0d. a = 0.26 m/s2

3. A particle has an initial velocity of (3i + 4j) m/s and a constant acceleration of (0.4i + 0.3j) m/s2. Its speed after 10 s is:a. 7√2 m/s b. 7 m/s c. 5 m/s d. 10 m/s

4. Two force vectors have magnitude 6 N and 8 N. Their resultant may have a magnitude:a. 5 N b. 10 N c. 13 N d. 16 N

5. In case of a uniform circular motion, which of the following physical quantities remains constant?

a. Speed b. Acceleration c. Kinetic energy d. Momentum

6. A particle is projected with a speed of 20 m/s at an angle 60o above horizontal. At the highest point of its trajectory:a. X = 10 m b. Y = 10 m c. R = 10 m d. Y = 15 m

7. When a bicycle is in motion, the force of friction exerted by the ground on the two wheels may be such that it acts:a. In the backward direction on the front wheel and in the forward direction on the rear wheelb. In the forward direction on the front wheel and in the backward direction on the rear wheelc. In the backward direction on both front and rear wheelsd. In the forward direction on both front and rear wheels.

8. A particle moves in the x-y plane under the influence of a force such that its linear momentum is p = A [ i cos (kt) – j sin (kt) ], where A and k are constants. The angle between the force and the momentum is:a. 0o b. 30o c. 45o d. 90o

9. Two weights W1 and W2 are suspended from the ends of a light string passing over an ideal pulley. If the pulley is pulled up with acceleration g, the force required to pull is:

a. b. c. d.

10. A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes an uncompressed spring and compresses it till the block is motionless. The kinetic frictional force is 15 N and spring constant is 10,000 N/m. The spring compresses by:a. 8.5 cm b. 5.5 cm c. 2.5 cm d. 11.0 cm

11. A block of mass 10 kg is kept n a rough horizontal surface of μ = 1/√3. What is the minimum force required to pull the block?a. 50 N b. 57.7 N c. 5.77 N d. 100 N

12. A force F = - K (y i + x j) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0), and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particle is:a. –2Ka2 b. 2Ka2 c. –Ka2 d. Ka2 .

13. Two springs have their force constants as K1 and K2 (K1 > K2). The work done, when both are stretched by the same amount of length, will be:a. Equal b. Greater for K1 c. Greater for K2 d. Given data is incomplete.

14. A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the center. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is:a. √ (u2 – 2gL) b. √(2gL) c. √(u2 – gL) d. √(2u2 – 2gL)

15. Two masses of 1 gm and 4 gm are moving with KE in the ratio of 4:1. What is the ratio of their linear momenta?a. 1:1 b. 1:2 c. 4:1 d. 6:1

16. A particle starts moving from the position of rest under a constant acceleration. It travels a distance x in the first 10 sec and distance y in the next 10 sec, then:a. y = x b. y = 2x c. y = 3x d. y = 4x.

17. If the radius of earth were to shrink by 1%, its mass decreases by 2%, the acceleration due to gravity on the earth’s surface would:a. Increa

se by 2%b. Remain same c. Decrease by 2%

d. Decrease by 3%

18. Which of the following quantities can be written in SI units in kg m2 A-2 s-3 a. Resistance b. Inductance c. Capacitance d. Magnetic flux

19. A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the water in km/hr is:a. 1 b. 3 c. 4 d. √14

20. A false balance has equal arms. An object weighs W1 when placed in one pan and W2 when placed in the other pan. The true weight W of the object is:a. (W1 x W2)1/2 b. (W1

2 + W22)1/2 c. (W1 + W2)/2 d. W1W2 / (W1 + W2)

21. Apparent weight of a body in an elevator is more than rest weight if elevator is:a. Going up and slowing downb. Going up and speeding up

c. Going down and slowing downd. Going down and speeding up

22. A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force constant of:a. 2k / 3 b. 3k / 2 c. 3k d. 6k

23. block ofmass m slides down an inclined plane which makes an angle with the horizontal. The coefficient of friction between the block and the plane is . The force on the block is:a. mg cos b. mg (sin - cos ) c. √(2 + 1) mg cos d. mg cos /√(2 + 1)

24. A particle starts from rest and moves along a straight line according to the graph. Then:a. Vmax = 16 m/sb. Vmax = 24 m/s

c. aav = 2 m/s2 d. amax = 12 m/s2

25. In the previous question (Q -24), distance traveled is:a. 12 mb. 24 m

c. 128/3 md. 128 m

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Answers Test-1 Mechanics

1 a, b, c 6 c, d 11 a 16 c 21 b, c2 a, d 7 a, c 12 c 17 b 22 b3 a 8 d 13 b 18 a 23 b4 a, b, c 9 c 14 d 19 b 24 b, c5 a, c 10 b 15 a 20 c 25 d

Date- 05-09-10