SectionI
Single Correct Option
Q.1. Which one of the following has the dimensions of pressure?
(a) [ML^{2}T^{2}]
(b) [M^{1} L^{1}]
(c) [MLT^{2}]
(d) [ML^{1}T^{2}]
Ans. (d)
Sol:
∴
= [ML^{1}T^{2}]
Q.2. Which of the following will have the dimensions of time
(a) LC
(b) R/L
(c) L/R
(d) C/L
Ans. (c)
W = I^{2} Rt
∴
∴
Using Eq. (i)
[R] = [L]/[T]
i.e., [T] = [L/R]
Option is correct.
Q.3. The force F on a sphere of radius a moving in a medium with velocity v is given by F = 6πηa v. The dimensions ofη are
(a) [ML^{3}]
(b) [MLT^{2}]
(c) [MT^{ 1}]
(d) [ML^{1}T^{1}]
Ans: (d)
F= 6π ηav
∴
Q.4. The dimensional formula for magnetic flux is
(a) [ML^{2}T ^{2}A^{1}]
(b) [ML^{3}T^{2}A^{2}]
(c) [M^{0} L^{2}T^{2}A^{2}]
(d) [ML^{2}T^{1}A^{2}]
Ans: (a)
φ = Li
∴ [φ] = [L] [i]
=[ML^{2} T^{2} A^{2}] [A]
=[ML^{2} T^{2} A^{1}]
Option is correct.
Q.5. Dimensions of linear impulse are
(a) [ML^{2}T^{3}]
(b) [ML^{2}]
(c) [MLT ^{1}]
(d) [MLT^{2}]
Ans. (c)
Linear impulse (I) = F × Δt
[I ] = [MLT^{2}] [T]
= [MLT^{}^{1}]
Q.6. What is the dimensional formula of gravitational constant?
(a) [ML^{2}T^{2}]
(b) [ML^{1}T^{ 1}]
(c) [M^{1}L^{3} T^{2}]
(d) None of these
Ans. (c)
Q.7.Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimension of permeability is
(a) [M^{1}LT^{2}A]
(b) [ML^{2}T^{2}A^{1}]
(c) [MLT^{ 2}A^{2}]
(d) [MLT^{ 1} A^{1}]
Ans. (c)
Q.8. The equation of a wave is given bywhere ω is angular velocity and v is the linear velocity. The dimensions of k will be
(a) [T^{2}]
(b) [T^{1}]
(c) [T]
(d) [LT]
Ans. (c)
Q.9. A force is given by F = at + bt^{2}
where t is the time. The dimensions of a and b are
(a) [MLT^{ 4}] and [MLT^{ 1}]
(b) [MLT^{1}] and [MLT^{0}]
(c) [MLT^{3}] and [MLT ^{4}]
(d) [MLT ^{3}] and [MLT^{0}]
Ans. (c)
Q.10. The dimensional formula for Planck’s constant and angular momentum are
(a) [ML^{2}T^{2}] and [MLT^{1}]
(b) [ML^{2}T^{1}] and [ML^{2}T^{1}]
(c) [ML^{3}T^{1}] and [ML^{2}T ^{2}]
(d) [MLT^{1}] and [MLT^{2}]
Ans. (b)
∴
Angular momentum (J) = nh/2π
[J] = [h] = [ML^{2} T^{1}]
Q.11. If the energy (E), velocity (v) and force (F) be taken as fundamental quantities, then the dimensions of mass will be
(a) Fv^{2} (b) Fv^{1} (c) Ev^{2} (d) Ev^{2}
Ans. (c)
[Energy] = [ML^{2}T^{2}]
= [M] [LT^{1}]^{2}
∴ [Mass] = [Ev^{2}]
Option is correct.
Q.12. The dimension of (ε_{0} is the permittivity of free space and E is electric field), is
(a) [ML^{2}T^{1}]
(b) [ML^{ 1}T^{2}]
(c) [ML^{2}T^{2}]
(d) [MLT^{1}]
Ans. (b)
= Energy density = Energy/Volume
∴
= [ML^{1} T^{2}]
Q.13. The dimensions of a/b in the equation 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}]
Ans. (b)
Sol: [a] = [T^{2}]
∴
Q.14. Dimension of velocity gradient is
(a) [M°L°T^{1}]
(b) [ML^{ 1}T^{1}]
(c) [M°LT^{1}]
(d) [ML°T^{1}]
Ans. (a)
Sol: Velocity gradient = dv/dx
[Velocity gradient]
= [T^{1}]
= [M^{0} L^{0} T^{1}]
Q.15. If force F, length Land time T are taken as fundamental units, the dimensional formula for mass will be
(a) [FL^{ 1}T^{2}]
(b) [FLT^{2}]
(c) [FL^{ 1}T^{1}]
(d) [FL^{5}T^{2}]
Ans: (a)
[Force] = [MLT^{2}]
Q.16. Which of the following is the dimension of the coefficient of friction? (a) [M^{2} L^{2}T]
(b) [M° L° T°]
(c) [ML^{2}T^{2}]
(d) [M^{2} L^{2}T^{2}]
Ans. (b)
Sol: Coefficient of friction (μ)
∴ [μ] = [M^{0} L^{0} T^{0}]
Option is correct.
Q.17. If C and R denote capacitance and resistance, then dimensions of CR will be
(a) [M°L°TA°]
(b) [ML°TA^{2}]
(c) [ML°TA^{2}]
(d) [ML°T^{2}A^{2}]
Ans: (a)
q = CV
and V = iR
∴ q = iCR
it = iCR
⇒ [CR] = [t] = [M^{0} L^{0} T A^{0}]
Q.18. The unit of permittivity of free space, ε_{0} is
(a) coulomb/newtonmetre
(b) newtonmetre^{2}/coulomb^{2}
(c) coulomb^{2}/newtonmetre^{2}
(d) coulomb^{2} /(newton metre)^{2}
Ans: (b)
∴ Unit of ε_{0} = Newtonmetre^{2} /coulomb^{2}.
Q.19. The ratio of the dimensions of Planck’s constant and that of the moment of inertia is the dimension of
(a) frequency
(b) velocity
(c) angular momentum
(d) time
Ans. (a)
Angular momentum (J) = nh/2π
∴
Q.20. The velocity v of a particle at time t is given by where a, b and c are constants. The dimensions of a, b and c are respectively
(a) [LT^{2}], [L] and [T]
(b) [L^{2}], [T] and [LT^{2}]
(c) [LT^{2}], [LT] and [L]
(d) [L], [LT] and [T^{2}]
Ans. (a)
[c] = [T]
or [b] = [LT^{1}] [T] = [L]
[at] = [v] = [LT^{1}]
⇒ [a] = [LT^{2}]
Q.21. Given that where y and x are measured in metres. Which of the following statements is true ?
(a) The unit of λ is same as that of x and A
(b) The unit of λ, is same as that of x but not of A
(c) The unit of c is same as that of 2π/λ
(d) The unit of (ct  x) is same as that of 2π/λ
Ans. (a)
∴ [x] = [λ] = [L]
Further, y = A sinθ
∴ [A] = [y] = [L]
Q.22. The physical quantity having the dimensions [M^{1}L^{3}T^{3}A^{2}] is
(a) resistance
(b) resistivity
(c) electrical conductivity
(d) electromotive force
Ans. (a)
[X] = [M^{1} L^{3} T^{3} A^{2}]
∴ X is resistance. [∴W = i^{2} Rt]
Q.23. The torque of force newton acting at the point metre about origin is (in Nm)
(a)
(b)
(c)
(d)
Ans. (b)
Q.24. If a unit vector is represented by the value of c is
(a) 1
(b) √0.11
(c) √0.01
(d) 0.39
Ans: (b)
Q.25. are two vectors such that he angle between vectors is
Ans.
Q.26. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
(a) are not equal to each other in magnitude
(b) cannot be predicted
(c) are equal to each other
(d) are equal to each other in magnitude
Ans. (d)
Q.27. Which one of the following is a scalar quantity?
(a) Displacement
(b) Electric field
(c) Acceleration
(d) Work
Ans: (d)
Work is a scalar quantity.
Q.28. Which one of the following is not the vector quantity?
(a) Torque
(b) Displacement
(c) Velocity
(d) Speed
Ans: (d)
Q.29. What is the dot product of two vectors of magnitude 3 and 5, if angle between them is 60°?
(a) 5.2
(b) 7.5
(c) 8.4
(d) 8.6
Ans: (b)
and angle between is 60°.
∴
= 7.5
Q.30. Two vectors are such that and A^{2} + B^{2} = C^{2}.
If 0 is the angle between positive direction of then the correct statement is
(a) θ = π
(b) θ = 2π/3
(c) θ = 0
(d) θ = π/2
Ans: (d)
∴
or
or
or
or
or cos θ = 0
or θ = π/2
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