THIS TEST CONTAINS 50 NUMBER OF QUESTIONS EACH OF MARK 4. TOTAL MARKS OF THE TEST IS 200 AND REQUIRED TIME IS 1 HOUR 30 MINUTES. YOU CAN USE THE ‘NEXT’ BUTTON TO SELECT THE NEXT QUESTION OR SIMPLY USE THE NUMBERS SHOWING ABOVE THE QUESTION. YOU CAN SKIP ANY QUESTION. AFTER COMPLETION OF TEST CLICK ‘QUIZ SUMMARY’ BUTTON TO VIEW YOUR ATTEMPT STATUS. THEN CLICK ‘FINISH QUIZ’ BUTTON. THE TEST WILL BE AUTOMATICALLY FINISHED IF THE TIME IS OVER. YOU CLICK THE ‘RESULT’ BUTTON TO VIEW YOUR RESULT. YOU CAN CLICK ‘VIEW QUESTION’ BUTTON TO VERIFY YOUR ANSWER.
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1. A physical quantity of the dimensions of length that can be formed out of c, G and is [c is velocity of light, G is the universal constant of gravitation and e is charge]
B.
C.
D.
2. Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
A.
B.
C.
D.
3. If dimensions of critical velocity v_{c }of a liquid flowing through a tube are expressed as [η^{x }ρ^{y} r^{z}] where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y, and z are given by
A. 1, 1, 1
B. 1, 1, 1
C. 1, 1, 1
D. 1, 1, 1
4. If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be
A. [EV ^{2}T ^{2}]
B. [E ^{2}V ^{1}T ^{3}]
C. [EV ^{2}T ^{1}]
D. [EV ^{1}T ^{2}]
5. If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are
A. [FVT ^{1}]
B. [FVT ^{2}]
C. [FV ^{1}T ^{1}]
D. [FV ^{1 }T]
6. In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows p = . The % error in P is
A. 7%
B. 4%
C. 14%
D. 10%
7. The pair of quantities having same dimensions is
A. Impulse and Surface Tension
B. Angular momentum and Work
C. Work and Torque
D. Young’s modulus and Energy
8. The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
A. kg m s^{1}
B. kg m s^{2 }
C. kg s^{1}
D. kg s
9. The dimensions of (µ_{0}ԑ_{0})^{1/2} are
A. [L^{1/2}T ^{1/2}]
B. [L^{1}T]
C. [LT ^{1}]
D. [L^{1/2}T^{1/2}]
10. The density of a material in C.G.S. system of units is 4 gcm^{3}. In a system of units, in which the unit of length is 10 cm and the unit of mass is 100 g, the value of density of material will be
A. 0.04
B. 0.4
C. 40
D. 400
11. The dimension of ԑ_{0}E^{2}, where ԑ_{0} is permittivity of free space and E is electric field, is
A. [ML^{2}T ^{2}]
B. [ML^{1}T ^{2}]
C. [ML^{2}T ^{1}]
D. [MLT ^{1}]
12. A student measures the distance traversed in free fall of a body, initially at rest, in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e_{1} and e_{2} respectively, the percentage error in the estimation of g is
A. e_{2 }– e_{1}
B. e_{1} + 2e_{2}
C. e_{1} + e_{2}
D. e_{1} – 2e_{2}
13. If the dimensions of a physical quantity are given by M^{a}L^{b}T^{c}, then the physical quantity will be
A. velocity if a = 1, b = 0, c = 1
B. acceleration if a = 1, b = 1, c = 2
C. force if a = 0, b = 1, c = 2
D. pressure if a = 1, b = 1, c = 2
14. If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
A. 8%
B. 2%
C. 4%
D. 6%
15. Which two of the following five physical parameters have the same dimensions?
(1) energy density (2) refractive index (3) dielectric constant (4) Young’s modulus (5) magnetic field
A. 1 and 4
B. 1 and 5
C. 2 and 4
D. 3 and 5
16. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
A. [ML^{2}T ^{2}]
B. [ML^{2}T ^{1}I^{– 1}]
C. [ML^{2}T ^{3}I ^{2}]
D. [ML^{2}T ^{3}I ^{1}]
17. The velocity v of a particle at time t is given by v = at + where a, b, and c are constants. The dimensions of a, b, and c are
A. [L], [LT] and [LT ^{2}]
B. [LT ^{2}], [L] and [T]
C. [L^{2}], [T] and [LT ^{2}]
D. [LT ^{2}], [LT] and [L]
18. Which pair do not have equal dimensions?
A. Energy and torque
B. Force and impulse
C. Angular momentum and Planck constant
D. Elastic modulus and pressure
19. The dimensional formula of magnetic flux is
A. [M^{0}L^{2}T ^{2}A^{2}]
B. [ML^{0}T ^{2}A^{2}]
C. [ML^{2}T ^{2}A^{1}]
D. [ML^{2}T ^{1}A^{3}]
20. An equation is given here [P + ] = where P = pressure, V = Volume and Ѳ = Absolute temperature. If a and b are constant, the dimensions of a will be
A. [ML^{5}T ^{1}]
B. [ML^{5}T^{1}]
C. [ML^{5}T ^{2}]
D. [ML^{5}T^{2}]
21. The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and lengths are 3% and 2% respectively, the maximum error in the measurement of density would be
A. 12%
B. 14%
C. 7%
D. 9%
22. Which of the following dimensions will be the same as that of time? [where L = inductance, R = resistance, C = capacitance]
A. L/R
B. C/L
C. LC
D. R/L
23. The ratio of the dimensions of Planck’s constant and that of moment of inertia is the dimensions of
A. time
B. frequency
C. angular momentum
D. velocity
24. The dimensions of RC is
A. square of time
B. square of inverse time
C. time
D. inverse time
25. Percentage errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be
A. 8%
B. 2%
C. 12%
D. 10%
26. Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of oil is given by η = where v is the velocity of oil at a distance x from the axis of the tube. The dimensions of η are
A. [M^{0}L^{0}T^{0}]
B. [MLT ^{1}]
C. [ML^{2}T ^{2}]
D. [ML^{1}T^{– 1}]
27. P represents radiation pressure, c represents speed of light and S represents radiation energy striking per unit area per sec. The nonzero integers x, y, z such that P^{x}S^{y}C^{z} is dimensionless are
A. x = 1, y = 1, z = 1
B. x = 1, y = 1, z = 1
C. x = 1, y = 1, z = 1
D. x = 1, y = 1, z = 1
28. A certain body weighs 22.42 g and has a measured volume of 4.7 cc. The possible error in the measurement of mass and volume are 0.01 g and 0.1 cc. Then maximum error in the density will be
A. 22%
B. 2%
C. 0.2%
D. 0.02%
29. The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation
f = am^{x}k^{y}, where a is a dimensionless constant. The values of x and y are
A. x = , y =
B. x = – , y = –
C. x = , y = –
D. x = – , y =
30. The dimensions of in the equation P = where P is pressure, x is distance and t is time are
A. [M^{2}LT ^{3}]
B. [MT ^{2} ]
C. [LT ^{3} ]
D. [ML^{3}T^{ 1}]
31. Which of the following combinations of three different physical quantities P, Q, R can never be a meaningful quantity?
A. PQ – R
B.
C.
D.
32. Dimensional formula of selfinductance is
A. [MLT ^{2}A ^{2}]
B. [ML^{2}T ^{1}A ^{2}]
C. [ML^{2}T ^{2}A ^{2}]
D. [ML^{2}T ^{2}A ^{1}]
33. The dimensional formula of torque is
A. [ML^{2}T ^{2}]
B. [MLT ^{2}]
C. [ML^{1}T ^{2}]
D. [ML^{2}T ^{2}]
34. In the relation P = where P is pressure, Z is distance, k is Boltzmann constant and is the temperature. The dimensional formula of will be
A. [M^{0}L^{2}T^{0}]
B. [M^{1}L^{2}T^{1}]
C. [M^{1}L^{0}T^{1}]
D. [M^{0}L^{2}T^{1}]
35. The velocity of a body moving in viscous medium is given by v = where t is time, A and B are constants. Then the dimensions of A are
A. [M^{0}L^{0}T^{0}]
B. [M^{0}L^{1}T^{0}]
C. [M^{0}L^{1}T ^{2}]
D. [M^{1}L^{1}T^{1}]
36. A body of mass m = 3.513 kg is moving along the xaxis with a speed of 5.00 . The magnitude of its momentum is recorded as (in kg)
A. 17.6
B. 17.565
C. 17.56
D. 17.57
37. In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half a degree (= 0.5°), then the least count of the instrument its
A. half minute
B. one degree
C. half degree
D. one minute
38. A screw gauge gives the following reading when used to measure the diameter of a wire.
Main scale reading: 0 mm
Circular scale reading: 52 divisions
Given that 1 mm on main scale corresponds to l 00 divisions of the circular scale. The diameter of wire from the above data is
A. 0.052 cm
B. 0.026 cm
C. 0.005 cm
D. 0.52 cm
39. The period of oscillation of a simple pendulum is T = . Measured value of l is 20.0 cm known to 1 mm accuracy and time for 100 oscillations for the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is
A. 1%
B. 5%
C. 2%
D. 3%
40. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be
A. (92 1.5) s
B. (92 3) s
C. (92 2) s
D. (92 5.0) s
41. A screw gauge with a pitch of 0.5 mm and a circular scale with 50 divisions is used to measure the thickness of a thin sheet of aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the 45th division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is 0.5 mm and the 25th division coincides with the main scale line?
A 0.70 mm
B. 0.50 mm
C. 0.75 mm
D. 0.80 mm
42. In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is 0.2 s at the end of 4 s, then the error in estimation of height of bridge will be (neglect the water resistance, i.e., thrust)
A. 19.68 m
B. 17.22 m
C. 7.84 m
D. 12.22 m
43. A physical quantity X is given by X = . The percentage errors in the measurements of k, I, m and n are 1%, 2%, 3% and 4% respectively. The value of X is uncertain by
A. 8%
B. 10%
C. 12%
D. none of these
44. In terms of basic units of mass (M), length(L), time (T) and charge (C), the dimensions of magnetic permeability of vacuum () would be
A. []
B. []
C. []
D. []
45. The pressure on a square plate is measured by measuring the force on the plate and the length of the side of the plate by using the formula p = . If the maximum errors in the measurement of force and length are 4% and 2% respectively, then the maximum error in the measurement of pressure is
A. 1%
B. 2 %
C. 8%
D. 10%
46. The force F is given by expression F = Acos(BX) + Csin(Dt), where x is the displacement and t is the time. Then, dimension of is same as that of
A. velocity []
B. angular velocity []
C. angular momentum []
d. velocity gradient []
47. Of the following quantities, the same dimensional quantities are
(1) energy per unit volume (2) force per unit area
(3) product of voltage and charge per unit area (4) angular momentum per unit mass
A. 1, 3
B. 1, 3, 4
C. 1, 4
D. 1,2
48. In an experiment to verify Poiseullie’s law [] where the symbols have their usual meanings, the maximum error that enters in calculating the coefficient of viscosity is due to measurement of
A. pressure difference
B. length of the tube l
C. volume rate of ﬂow V
D. radius of the tube a
49. Assertion: When we change the unit of measurement of a quantity, its numerical value changes.
Reason: Smaller the unit of measurement, smaller is its numerical value.
A. Both assertion and reason are true and reason is the correct explanation of assertion.
B. Both assertion and reason are true but reason is not the correct explanation of assertion.
C. Assertion is true but reason is false.
D. Both assertion and reason are false.
50. Assertion: The error in the measurement of radius of the sphere is 0.3%, The permissible error in its surface area is 0.6%.
Reason: The permissible error is calculated by the formula = .
A Both assertion and reason are true and reason is the correct explanation of assertion.
B Both assertion and reason are true but reason is not the correct explanation of assertion.
C Assertion is true but reason is false.
D Both assertion and reason are false.