Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
A physical quantity of the dimensions of length that can be formed out of c, G and e²/(4πε₀) is [c is velocity of light, G is universal constant of gravitation and e is charge]:
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 the screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is:
Which one of the following statements is incorrect?
The main scale of a vernier calliper has n divisions/cm. n divisions of the vernier scale coincide with (n-1) divisions of the main scale. The least count of the vernier calliper is:
In an experiment, the percentage errors in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage error in the measurement X, where X = A^(1/2) B² / (C^(1/3) D³), will be:
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The unit of thermal conductivity is:
A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is:
Taking into account the significant figures, what is the value of 9.99 m - 0.0099 m?
Dimensions of stress are:
A screw gauge gives the following readings when used to measure the diameter of a wire: Main scale reading: 0 mm; Circular scale reading: 52 divisions. Given that 1 mm on the main scale corresponds to 100 divisions on the circular scale, the diameter of the wire is:
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities, find the dimensions of energy.
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of:
Plane angle and solid angle have:
The area of a rectangular field (in m²) of length 55.3 m and breadth 25 m, after rounding off the value for correct significant digits, is:
The dimensions [MLT⁻²A⁻²] belong to the:
Match List-I with List-II: List-I (a) Gravitational constant (G) (b) Gravitational potential energy (c) Gravitational potential (d) Gravitational intensity List-II (i) [L²T⁻²] (ii) [M⁻¹L³T⁻²] (iii) [LT⁻²] (iv) [ML²T⁻²] Choose the correct match:
The diameter of a spherical bob, measured with vernier callipers, yielded the values: 3.33 cm, 3.32 cm, 3.34 cm, 3.33 cm and 3.32 cm. The mean diameter to appropriate significant figures is:
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:
The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
The mechanical quantity, which has dimensions of the reciprocal of mass (M⁻¹) is:
A force defined by F = αt + βt² acts on a particle at a given time t. The factor which is dimensionless, if α and β are constants, is:
In a vernier callipers, (N+1) divisions of the vernier scale coincide with N divisions of the main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:
The quantities which have the same dimensions as those of solid angle are:
The diameter of a spherical object is measured with a vernier caliper whose 10 vernier scale divisions (VSD) equal 9 main scale divisions (MSD). The least MSD is 0.1 cm and the zero of the vernier scale is at x = 0.1 cm when the jaws are closed. If the main scale reading for the diameter is M = 5 cm and the coinciding vernier division is 8, the measured diameter after zero-error correction is:
A balloon is made of a material of surface tension S and its inflation outlet (from where gas is filled) 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 in time T. If the speed v(r) of gas coming out depends on r as r^a and T ∝ S^α A^β ρ^γ R^δ, then:
A physical quantity P is related to four observations a, b, c and d as P = a³b²/(c·√d). The percentage errors of measurement in a, b, c and d are 1%, 3%, 2% and 4% respectively. The percentage error in the quantity P is:
In a vernier calliper, 20 VSD coincide with 16 MSD (each division of length 1 mm). The least count of the vernier calliper is:
The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in the new unit is:
Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the significant figures in view, the density of the material of the cube can be best expressed as X × 10³ kg m⁻³, where the value of X is:
Let $\sigma_s$, $k_B$ and $b$ represent the Stefan–Boltzmann constant, Boltzmann constant and Wien's displacement-law constant respectively. The dimension of $\sigma_s\,k_B^{-1}\,b$ is:
Which of the following measurements requires ‘index correction’?
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