Dimensions of resistance in an electrical circuit, in terms of the dimension of mass M, of length L, of time T and of current I, would be:
[ML2T-3I-1]
[ML2T-2]
[ML2T-1I-1]
[ML2T-1I-1]
D.
[ML2T-1I-1]
Resistance
The physical quantity of the dimensions of length that can be formed out of c, G and e/4πε0 is [c is the velocity of light, G is the universal constant of gravitation and e is charge]
A.
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.
According to principle of homogeneity of dimensions, the dimensions of all the terms in a physical expression should be same.
The given expression is
From principle of homogeneity
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 screw gauge has a zero error of –0.004 cm, the correct diameter of the ball is
0.521 cm
0.525 cm
0.529 cm
0.053
C.
0.529 cm
Diameter of the ball
= MSR + CSR x (least count) - zero error
= 0.5 cm + 25 x 0.001 - (-0.004)
= 0.5 + 0.025 + 0.004
= 0.529 cm
The length, breadth and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm. The volume of the block according to the idea of significant figures should be
1 × 102 cm3
2 × 102 cm3
1.76 × 102 cm3
None of these
B.
2 × 102 cm3
Using relation for volume
Given:- length of a block = 12 cm
breadth of a block = 6 cm
thickness of a block = 2.45cm
V =length × breadth × thickness
=12 × 6 × 2.45 = 176.4
=1.764 ×102 cm3
The minimum number of significant figures is 1 in thickness, hence the volume will contain only one significant figure.
Therefore V= 2 ×102 cm3