General
✓✗The dimensional formula of surface tension is
- [MLT−2]
- [MT−2]
- [ML−1T−2]
- [ML2T−2]
General
✓✗A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled in it) has small area A. It is filled with a gas of density ρ and takes a spherical shape of radius R. When the gas is allowed to flow freely out of it, its radius r changes from R to 0 (zero) in time T. If the speed v(r) of gas coming out of the balloon depends on r as ra and T ∝ SαAβργRδ, then
- \( a = -\dfrac{1}{2},\ \alpha = -\dfrac{1}{2},\ \beta = -1,\ \gamma = \dfrac{1}{2},\ \delta = \dfrac{7}{2} \)
- \( a = \dfrac{1}{2},\ \alpha = \dfrac{1}{2},\ \beta = -\dfrac{1}{2},\ \gamma = \dfrac{1}{2},\ \delta = \dfrac{7}{2} \)
- \( a = \dfrac{1}{2},\ \alpha = \dfrac{1}{2},\ \beta = -1,\ \gamma = 1,\ \delta = \dfrac{3}{2} \)
- \( a = -\dfrac{1}{2},\ \alpha = -\dfrac{1}{2},\ \beta = -1,\ \gamma = \dfrac{1}{2},\ \delta = \dfrac{5}{2} \)
General
✓✗A vernier callipers has a positive zero error of 0.02 cm. If the observed reading is 3.56 cm, the correct reading is
- 3.56 cm
- 3.54 cm
- 3.52 cm
- 3.58 cm
General
✓✗The dimensional formula of specific heat capacity is
- [ML2T−2K]
- [L2T−1K−1]
- [ML2T−2K−1]
- [L2T−2K−1]
General
✓✗The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation \( f = a\,m^x k^y \), where a is a dimensionless constant. The value of x and y are
- \( x = \dfrac{1}{2},\ y = \dfrac{1}{2} \)
- \( x = -\dfrac{1}{2},\ y = -\dfrac{1}{2} \)
- \( x = \dfrac{1}{2},\ y = -\dfrac{1}{2} \)
- \( x = -\dfrac{1}{2},\ y = \dfrac{1}{2} \)
General
✓✗The value of gravitational acceleration g = 9.8 m s−2 in km h−2 is about
- 3.5 × 104
- 9.8 × 103
- 1.27 × 103
- 1.27 × 105
General
✓✗The mass of a box is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to it. The total mass of the box, to correct significant figures, is
- 2.3432 kg
- 2.343 kg
- 2.34 kg
- 2.3 kg
General
✓✗If x = at + bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the units of b is
- km/s
- km s
- km/s2
- km s2
General
✓✗The dimensional formula of torque is the same as that of
- momentum
- work
- power
- force
General
✓✗The number of significant figures in 2.64 × 1024 kg is
- 3
- 2
- 24
- 4
General
✓✗The dimensional formula of impulse is
- [MLT−2]
- [ML2T−2]
- [ML2T−1]
- [MLT−1]
General
✓✗Which of the following dimensions will be the same as that of time?
- \( \dfrac{L}{R} \)
- \( \dfrac{C}{L} \)
- \( LC \)
- \( \dfrac{R}{L} \)
General
✓✗A physical quantity of the dimensions of length that can be formed out of c, G and \( \dfrac{e^2}{4\pi\varepsilon_0} \) is
[c is velocity of light, G is the universal constant of gravitation and e is charge]
[c is velocity of light, G is the universal constant of gravitation and e is charge]
- \( c^2\left[G\,\dfrac{e^2}{4\pi\varepsilon_0}\right]^{1/2} \)
- \( \dfrac{1}{c^2}\left[\dfrac{e^2}{G\,4\pi\varepsilon_0}\right]^{1/2} \)
- \( \dfrac{1}{c}\,G\,\dfrac{e^2}{4\pi\varepsilon_0} \)
- \( \dfrac{1}{c^2}\left[G\,\dfrac{e^2}{4\pi\varepsilon_0}\right]^{1/2} \)
General
✓✗The dimensional formula of the Stefan-Boltzmann constant is
- [MLT−3K−4]
- [MT−2K−4]
- [ML2T−3K−4]
- [MT−3K−4]
General
✓✗The dimensional formula of Young's modulus is the same as that of
- force
- pressure
- work
- momentum