Question – 1

1. Dimensional formula of a physical quantity is given as M^{x}L^{y}T^{z}. If the dimensional formula of the physical quantity is the same as that of force, what would be the value of x+y+z ?

- A. 0
- B. -1
- C. -4
- D. 1
- E. 2
- Answer:A
- Answer Explanation:Dimensional formula of force is MLT
^{-2}Dimensional formula of the physical quantity is same as that of force; hence,M^{x}L^{y}T^{z}= MLT^{-2}.Now, equating the exponents of common terms (M, L and T),we getHence, x+y+z can be given asx+y+z =1+1-2 Or x+y+z =0Hence, A is the correct answer option

Question – 2

2. A vertical U tube contains water up to a height of 0.1 m (from the base). If the water of one side of the liquid column is lifted up and then released the liquid sets into oscillation, what is the time period of the oscillation?

- A. 0.72 s
- B. 0.63 s
- C. 0.345 s
- D. 0.512 s
- E. None of the given choices
- Answer:B
- Answer Explanation:T = 2?????(h/g)T = 2?????(0.1/9.8) Or T = 2?? X 0.101T = 6.28 X 0.101 Or T = 0.63sHence, B is the correct answer option.

Question – 3

3. What would be the Potential Energy stored in a spring of spring constant 20 N/m that is compressed by 2 cm?

- A. 2 X 10
^{-2}J - B. 10
^{-2}J - C. 4 X 10
^{-3}J - D. 7 X 10
^{-3}J - E. 8 X 10
^{-3}J - Answer:C
- Answer Explanation:PE = 1/2 kx
^{2}As the distance is given in cm we need to convert it into m.PE = 1/2 X 20 X (0.02)^{2}Or PE = 4 X 10^{-3}JouleHence, C is the correct answer option.

Question – 4

4. The weight of a block is 200 N in air. If the block is immersed completely in water, its weight becomes 120 N, what is the relative density of the block?

- A. 2.5
- B. 1.67
- C. 0.6
- D. 3.5
- E. 0.1
- Answer:A
- Answer Explanation:RD = weight of body in air / loss of weight in waterloss of weight in water = Actual weight in water – weight in water;Therefore, loss of weight in water = 200 – 120 = 80 N;RD = 200 / 80 = 2.5Hence, A is the correct answer option.

Question – 5

5. What would be the energy of the photon for which frequency is 2.4 X 10^{14} Hz?

- A. 2.77 X 10
^{-19}J - B. 1.2 X 10
^{-19}J - C. 6.6 X 10
^{-20}J - D. 1.6 X 10
^{-20}J - E. 1.6 X 10
^{-19}J - Answer:E
- Answer Explanation:E = h??E = 6.6 X 10
^{-34}X 2.4 X 10^{14}Or E = 15.84 X 10^{-20}JExpressing the result in standard from we getE = 15.84 X 10^{-19}JE is only option closet to the answer so it is the correct answer option.

Question – 6

6. A wave is in the frequency range of 40 Hz to 20000 Hz. What will be its range in terms of the time period?

- A. 2.5 X 10
^{-2}s to 5 X 10^{-5}s - B. 1.5 X 10
^{-2}s to 5.8 X 10^{-5}s - C. 1.5 X 10
^{-2}s to 4.5 X 10^{-5}s - D. 1 X 10
^{-2}s to 2 X 10^{-5}s - E. Not enough data is provided to predict the answer
- Answer:A
- Answer Explanation:T = 1/??For the frequency of 40 Hz,T = 1/40 Or,T = 0.025 sT = 2.5 X 10
^{-2}sFor the frequency of 20000 Hz,T = 1/20000 Or,T = 0.025 sT = 5 X 10^{-5}sHence, range of time period for the wave is given as2.5 X 10^{-2}s to 5 X 10^{-5}s. Hence, A is the correct answer option.

Question – 7

7. A capacitor charged to 100 V is connected through a resistance of . What is the heat produced in the resistance?

- A. 0.1 J
- B. 10 J
- C. 0.05 J
- D. 50 J
- E. Not enough data is provided to predict the answer
- Answer:C
- Answer Explanation: Heat produced in the resistance is equivalent to the energy stored in the capacitor.E = 1/2 CV
^{2}E = 1/2 X 10 X 10^{-6}X 100^{2}E = 0.05 JHence, C is the correct answer option.

Question – 8

8. Consider the figure given below in which the position time graph of three bodies A, B and C is shown.(x is the position and t is the time taken)Which of the following has zero displacement?

- A. A
- B. C
- C. B
- D. Both A and C
- E. Not enough data is provided to predict the answer
- Answer:C
- Answer Explanation:Displacement can be defined as the difference between the final position and the initial position. For both the bodies A and C, position is changing. Hence, final position is different from the initial position and so this will result non-zero value of displacement. Therefore, options A, C and D are incorrect. For body B, final position is the same as the initial position since the line is straight. Hence, displacement for the body B is zero. Thus, C is the correct answer option. In view of the above, option E is incorrect as well.

Question – 9

9. An object of height 5 cm is kept at 8 cm from a concave mirror. If the image is formed at 10 cm, what is height of the image?

- A. 4.25 cm
- B. 16 cm
- C. 6.25 cm
- D. 2.25 cm
- E. 4.5 cm
- Answer:C
- Answer Explanation:m = -(d
_{i}/ d_{o}) = h_{i}/ h_{o}-(10 / 8) = h_{i}/ 5 Or h_{i}= -6.25 cmNegative sign signifies that image is inverted. Hence, C is the correct answer option

Question – 10

10. A man of mass 65 kg stands on a weighing machine in a lift. If the lift is moving up with a uniform velocity of 7 m/s, what would be the weight of the man read by the machine?

- A. 656 N
- B. 455 N
- C. 398 N
- D. 612 N
- E. 637 N
- Answer:E
- Answer Explanation:When the lift moves up with a uniform velocity of 7 m/s, the acceleration will be zero (acceleration is time rate of change of velocity). That means, acceleration experienced by the man is zero hence, the man is in static equilibrium or no unbalanced force acts on it.W = mgW = 65 X 9.8 Or W = 637 NHence, E is the correct answer option

Question – 11

11. The Kinetic energy of a nitrogen molecule at 10^{o} C is 7.23 X 10^{-21} J. What will be the Avogadro’s number when gas constant is 8.31 J/mol/K?

- A. 4.88 X 10
^{23} - B. 2.28 X 10
^{23} - C. 1.15 X 10
^{21} - D. 5.53 X 10
^{23} - E. None of the given choices
- Answer:A
- Answer Explanation:KE = (3/2) (R/N) TAs the temperature is given in 10
^{o}C we need to convert it into Kelvin.7.23 X 10^{-21}= (3/2) X (8.31 / N) X 283N = (3/2) X (8.31/7.23 X 10^{-21}) X 283 Or N = 4.88 X 10^{23}Hence, A is the correct answer option

Question – 12

12. A water gallon of mass 500 kg is resting on a horizontal floor. What would be its normal reaction?

- A. 500 N
- B. 4900 N
- C. 5100 N
- D. 250 N
- E. 51.02 N
- Answer:B
- Answer Explanation:As the water gallon is resting on the floor, normal reaction will be balanced by the weight of the gallon itself. Therefore, Normal reaction = Weight of the gallon.Weight of the gallon is given as F = mgF = 500 X 9.8 Or F = 4900 NHence Normal reaction = 4900 NTherefore, B is the correct answer option.

Question – 13

13. A baseball is thrown vertically upwards with a velocity of 10 m/s. What is the distance of the baseball from the ground at its highest point during the flight? What is the velocity of the ball at the highest point?

- A. 50 m and 10 m/s
- B. 10.2 m and 0 m/s
- C. 5.1 m and 0 m/s
- D. 4.5 m and 5 m/s
- E. 7.5 m and 9.8 m/s
- Answer:C
- Answer Explanation:v
^{2}= u^{2}– 2gS (Negative sign is used because the ball is thrown against the Earth’s gravity)0 = 10^{2}– (2 X 9.8 X S) Or 2 X 9.8 X S = 100S = 100/(2 X 9.8) Or S = 5.1 mHence, C is the correct answer option.

Question – 14

14. A flywheel of mass 35 kg is rotating with an angular velocity of 7 rad/s. If energy amounting to 500 J is spent to increase the angular velocity of the flywheel to 14 rad/s, what is the moment of inertia of flywheel as a result of change in angular velocity?

- A. 5.5 kgm
^{2} - B. 7.8 kgm
^{2} - C. 6.8 kgm
^{2} - D. 4.5 kgm
^{2} - E. 8.2 kgm
^{2} - Answer:C
- Answer Explanation:W = KE
_{2}– KE_{1}KE = 1/2 I??^{2}Final Kinetic Energy is given as KE_{2}= 1/2 I??_{2}^{2}Initial Kinetic Energy is given as KE_{1}= 1/2 I??_{1}^{2}1/2 I (??_{2}^{2}– ??_{1}^{2}) = 500 Or 1/2 I (14_{2}^{2}– 7_{1}^{2}) = 500I = 6.8 kgm^{2}Hence, C is the correct answer option.

Question – 15

15. A man is standing in a lift that is accelerating upwards with an acceleration of 2.4 m/s^{2}. If the man is holding a spring balance having a load of 25 kg, what reading the balance would show now?

- A. 25.45 kg
- B. 60 kg
- C. 10.42 kg
- D. 30.45 kg
- E. 31.12 kg
- Answer:E
- Answer Explanation:The apparent weight of the load in a lift that is accelerating upwards is given asR = mg + maR = m(a + g) Or R = 25(2.4 + 9.8)R = 305 NThe apparent mass of the load is m= R/g or m= 305 / 9.8 or 31.12 kgHence, E is the correct answer option.