If T denotes the surface tension and R, the radius of a capillary tube, then the dimensions of T/R are the same as that of
1) pressure 2) energy 3) force 4) None of these Answer: 1) pressure Solution: T/R = MT-2/L = ML-1T-2 =... View Article
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The dimensions of intensity are
1) ML0T-3 2) M2L1T-2 3) ML2T-2 4) M2L2T-3 Answer: 1) ML0T-3 Solution: The intensity of a wave is defined as the... View Article
The dimensions of the pressure gradient are
1) ML-2T-2 2) ML2T-1 3) ML-1T-1 4) ML-1T-2 Answer: 1) ML-2T-2 Solution: Pressure gradient = dp/dx p= force/Area=ML−1T−2 Where, x=L =... View Article
The dimensional formula of propagation vector (K) is
1) [M0LT-1] 2) [M0L-1T0] 3) [M1L-1T0] 4) [M-1L-1T0] Answer: 2) [M0L-1T0] Solution: Propagation vector K = 2π/λ = 1/L = L-1... View Article
Fission of uranium by slow neutrons is used in
1) Rocket propulsion 2) Particle accelerator 3) Electric generator 4) Nuclear reactor Answer: 4) Nuclear reactor Solution: In a nuclear reactor,... View Article
Out of the following four-dimensional quantities, which one qualifies to be called a dimensional constant
1) Acceleration due to gravity 2) Surface tension of water 3) Weight of a standard kilogram mass 4) The velocity... View Article
What is the dimensional formula of thermal conductivity?
1) [MLT -1 θ -1 ] 2) [MLT -3 θ -1 ] 3) [M 2LT -3 θ -2 ] 4)... View Article
Which of the following sets of quantities have same dimensional formula?
1) Frequency, angular frequency and angular momentum 2) Surface tension, stress and spring constant 3) Acceleration, momentum and retardation 4)... View Article
The statement p → (q → p) is equivalent to
1) p → (p ˅ q) 2) p → (p ˄ q) 3) p → (p ↔ q) 4) p... View Article
The frequency f of vibration of mass m suspended from a spring of spring constant k is given by f = cmx ky where c is a dimensionless constant. The values of x and y are respectively
1) 1/2, 1/2 2) –1/2, 1/2 3) 1/2, –1/2 4) –1/2, –1/2 Answer: 2) –1/2, 1/2 Solution: by putting the dimensions... View Article
If voltage V = (100 ± 5 ) V and current I = ( 10 ± 0.2 ) A, the percentage error in resistance R is
1) 5.2% 2) 25% 3) 7% 4) 10% Answer: 3) 7% Solution: Resistance is the ratio of voltage used and the... View Article
If C is capacitance and q is charge, then the dimension of q2 /C is same as that of
1) work 2) angular momentum 3) force 4) torque and energy Answer: 1) work Solution: Energy = (1/2)CV2 = Q2/2C =... View Article
Position of a body with acceleration a is given by x = kam tn . Here, t is time. Find the values of m and n
1) m = 1, n = 1 2) m = 1, n = 2 3) m =2, n = 1... View Article
Which of the following sets have different dimensions?
1) Pressure, young’s modulus, stress 2) Emf, potential difference, electric potential 3) Heat, work done, energy 4) Dipole moment, electric... View Article
Find the dimensions of electric permittivity
1) [A2 M -1 L -3 T4] 2) [A2 M -1 L -3 T0] 3) [A M -1 L -3... View Article
If C, R, L and I denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are
(I) = CR (II) = L/R (III) = √LC (IV) = LI2 1) (I) and (II) 2) (I) and (III) 3)... View Article
Which of the following is dimensionless?
1) v2/rg 2) v2g/r 3) vg/r 4) v2rg Answer: 1) v2/rg Solution: \(\begin{array}{l}\frac{v^{2}r}{g}=\frac{(L^{1}T^{-1})^{2}L^{1}}{LT^{-2}}=L^{2}\end{array} \) \(\begin{array}{l}\frac{v^{2}}{rg}=\frac{(L^{1}T^{-1})^{2}}{L^{1}LT^{-2}}=M^{0}L^{0}T^{0}\end{array} \) \(\begin{array}{l}\frac{v^{2}g}{r}=\frac{(L^{1}T^{-1})^{2}LT^{-2}}{L^{1}}=L^{2}T^{-4}\end{array} \) \(\begin{array}{l}v^{2}rg =(L^{1}T^{-1})^{2}LT^{-2}L^{1}= L^{4}T^{-3}\end{array}... View Article
In a new system of units called star units, 1 kg* =10 kg, 1 m* =1 km and ls* =1min, what will be the value of 1 J in the new system?
1) 2.4 × 10-5 J* 2) 3.6 × 10-4 J* 3) 4.2 × 10-3 J* 4) 4.2 × 10-2 J*... View Article
The proposition (p ⇒ ~ p) ˄ (~ p ⇒ p) is a
1) Tautology and contradiction 2) Neither tautology nor contradiction 3) Contradiction 4) Tautology Solution: (3) Contradiction p ~ p p... View Article
~ (p ˅ q) ˅ (~ p ˄ q) is logically equivalent to
1) ~ p 2) p 3) q 4) ~ q Solution: (1) ~ p \(\begin{array}{l}\begin{array}{l} \sim(p \vee q) \vee(\sim p... View Article
