General
✓✗Which of the following pairs does NOT have the same dimensions?
- Momentum and impulse
- Power and energy
- Work and torque
- Stress and pressure
General
✓✗The dimensional formula of the Stefan-Boltzmann constant is
- [MLT−3K−4]
- [MT−2K−4]
- [ML2T−3K−4]
- [MT−3K−4]
General
✓✗The dimensions of \( \sqrt{\dfrac{k}{m}} \), where k is a spring constant and m is mass, are those of
- force
- frequency (angular)
- time
- velocity
General
✓✗The dimensional formula of frequency is the same as that of
- time period
- angular velocity
- acceleration
- velocity
General
✓✗The heat generated in a resistor is H = I2Rt. The percentage errors in I, R and t are 2%, 1% and 1% respectively. The maximum percentage error in H is
- 6%
- 5%
- 4%
- 8%
General
✓✗For the readings 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s, the mean absolute error is about
- 0.22 s
- 0.11 s
- 0.01 s
- 0.05 s
General
✓✗The dimensions of \( \dfrac{e^2}{4\pi\varepsilon_0 hc} \), where e is the electronic charge, h Planck's constant and c the speed of light, are
- [ML−1T−2]
- [LT−1]
- dimensionless
- [ML2T−1]
General
✓✗Which pair does NOT have equal dimensions?
- Energy and torque
- Force and impulse
- Angular momentum and Planck's constant
- Elastic modulus and pressure
General
✓✗The period of oscillation of a simple pendulum is \( T = 2\pi\sqrt{\dfrac{L}{g}} \). L is about 20.0 cm, known to 1 mm accuracy, and the time for 100 oscillations is 90 s measured with a watch of 1 s resolution. The accuracy in the determination of g is about
- 2%
- 1%
- 5%
- 3%
General
✓✗If C and R denote capacitance and resistance, the dimensional formula of CR is
- [M0L0T1]
- [M0L0T0]
- [M0L0T–1]
- not expressible in terms of MLT
General
✓✗In an experiment the measured values of a period are 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. The mean value of the period is
- 2.62 s
- 2.56 s
- 2.60 s
- 2.66 s
General
✓✗The least count of a vernier callipers in which 10 vernier divisions coincide with 9 main scale divisions of 1 mm each is
- 1 mm
- 0.01 mm
- 0.1 mm
- 0.9 mm
General
✓✗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 \( X = \dfrac{A^2 B^{1/2}}{C^{1/3} D^3} \), will be
- 10%
- \( \dfrac{3}{13} \)%
- 16%
- −10%
General
✓✗The ratio of the dimensions of Planck's constant and that of moment of inertia is the dimensions of
- velocity
- time
- angular momentum
- frequency
General
✓✗The escape velocity v from a planet depends on its mass M, radius R and gravitational constant G. By dimensional analysis, v ∝
- \( \sqrt{\dfrac{MR}{G}} \)
- \( \sqrt{\dfrac{GM}{R}} \)
- \( \dfrac{GM}{R} \)
- \( \sqrt{\dfrac{GR}{M}} \)