Q2: The quantities which have the same dimensions as those of solid angle are: [2024]
(a) strain and angle
(b) stress and angle
(c) strain and arc
(d) angular speed and stress
Ans: (a)
Solid angle has dimensions
Strain
Angle measured in radians is also dimensionless
Q3: A force defined by acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is: [2024]
(a) βt / α
(b) αt / β
(c) αβt
(d) αβ / t
Ans: (b)
From principle of homogeneity
Q1: A metal wire has mass (0.4 ± 0.002) g, radius (0.3 ± 0.001) mm and length (5 ± 0.02) cm. The maximum possible percentage error in the measurement of density will nearly be [2023]
(a) 1.2%
(b) 1.3%
(c) 1.6%
(d) 1.4%
Ans: (c)
Q4: The mechanical quantity, which has dimensions of reciprocal of mass (M^{−1}) is : [2023]
(a) angular momentum
(b) coefficient of thermal conductivity
(c) torque
(d) gravitational constant
Ans: (d)
Q1: The physical quantity that has the same dimensional formula as pressure is [2022]
(a) Coefficient of viscosity
(b) Force
(c) Momentum
(d) Young's modulus of elasticity
Ans: (d)
Q2: The percentage error in the measurement of g is : (Given that , s)
(a) 7%
(b) 2%
(c) 5%
(d) 3%
Ans: (d)
Q3: The dimensions [MLT^{–2}A^{–2} ] belong to the [2022]
(a) Selfinductance
(b) Magnetic permeability
(c) Electric permittivity
(d) Magnetic flux
Ans: (b)
Solution:
The dimensional formula of magnetic permeability is [MLT^{–2}A^{–2} ]
Q4: The area of a rectangular field (in m^{2 }) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is [2022]
(a) 1382
(b) 1382.5
(c) 14 * 10^{2 }
(d) 138 * 10^{1}
^{Ans: (c)}
^{Solution:}
Area = Length × Breadth
= 55.3 × 25 m^{2}
= 1382.5 m^{2}
= 14 × 10^{2} m^{2}
(Rounding off of two significant figures)
Q5: Match ListI with ListII
Choose the correct answer from the options given below [2022]
(a) (a)  (ii), (b)  (iv), (c)  (i), (d)  (iii)
(b) (a)  (ii), (b)  (iv), (c)  (iii), (d)  (i)
(c) (a)  (iv), (b)  (ii), (c)  (i), (d)  (iii)
(d) (a)  (ii), (b)  (i), (c)  (iv), (d)  (iii)
Ans: (a)
Solution:
Q1: A Screw Guage gives the following readings when used to measure the diameter of a wire.
Main scale reading = 0.0 mm
Circular scale reading = 52 divisions
Given that: 1 mm on the main scale corresponds to 100 divisions of the circular scale.
The diameter of the wire from the above data is: [2021]
(a) 0.026 cm
(b) 0.005 cm
(c) 0.52 cm
(d) 0.052 cm
Ans: (d)
Solution: Diameter of wire,
Q2: If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy. [2021]
(a) [F][A][T^{1}]
(b) [F][A^{1}][T]
(c) [F][A][T]
(d) [F][A][T^{2}]
Ans: (d)
Solution:
Q3: If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of : [2021]
(a) [M] [L^{0}] [T^{0}]
(b) [M^{2}] [L^{–2}] [T^{–1]}
(c) [M^{2}] [L^{–1}] [T^{0}]
(d) [M] [L^{–1}] [T^{–1}]
Ans: (c)
Solution:
E = energy = [ML^{2}T^{–2}]
G = Gravitational constant = [M^{–1}L^{3}T^{–2}]
So,
E/G = [E]/[G]
= ML2T–2/M^{–1}L^{3}T^{–2}
= [M^{2}L^{1}T^{0}]
Q1: A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. [2020]
The pitch of the screw gauge is :
(a) 0.25 mm
(b) 0.5 mm
(c) 1.0 mm
(d) 0.01 mm
Ans: (b)
Least count of screw gauge =
Q2: Taking into account of the significant figures, what is the value of 9.99 m0.0099 m? [2020]
(a) 9.980 m
(b) 9.9 m
(c) 9.9801 m
(d) 9.98 m
Ans: (d)
As per rule
least no. of place in decimal portion of any number 9.98
Q3: Dimensions of stress are : [2020]
(a) [ML^{2}T^{2}]
(b) ML^{0}T^{2}]
(c) ML^{1}T^{2}]
(d) MLT^{2}]
Ans: (c)
Q4: The energy required to break one bond in DNA is 10^{20} J. This value in eV is nearly : [2020]
(a) 0.6
(b) 0.06
(c) 0.006
(d) 6
Ans: (b)
Q1: In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where will be [2019]
(a)
(b) 16 %
(c) 10 %
(d) 10 %
Ans: (b)
Given
= 2% + 1%+ 1%+ 12%= 16%
Q1: A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of – 0.004 cm, the correct diameter of the ball is : [2018]
(a) 0.521 cm
(b) 0.525 cm
(c) 0.053 cm
(d) 0.529 cm
Ans: (d)
Solution:
Reading of screw gauge
= MSR + VSR × LC + zero error
= 0.5 cm + 25 × 0.001 cm + 0.004 cm
= 0.529 cm
Q1: A physical quantity of the dimensions of length that can be formed out of is velocity of light, G is universal constant of gravitation and e is charge] : [2017]
Q1: Planck's constant (h), speed of light in vacuum (c) and Newton's gravitional constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length ? [2016]
(a)
(b)
(c)
(d)
Ans: (a)
According to question,
L
[M^{0}LT^{0}] = [ML^{2}T^{1}]^{p} [LT^{1}]^{q} [M^{1}L^{3}T^{2}]^{r}
Equating power both sides, we get
p  r = 0 ......(1)
2p + q + 3r = 1 ......(2)
 p  q  2r = 0 ......(3)
Solving equation (1), (2), (3), we get
Q1: If dimensions of critical velocity v_{c} of a liquid flowing through a tube are expressed as 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 [2015]
Ans: (c)
Put dimensions of various quantities,
[M^{0}LT^{1}] = [ML^{1}T^{1}]^{x} [ML^{3}T^{0}]^{y} [M^{0}LT^{0}]^{z}
= [M^{x + y} L^{ x  3y + z} T^{ x}]
Equating power both sides, we get
x + y = 0;
 x  3y + z = 1;
 x =  1
On solving, we get
x = 1, y = 1, z = 1
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