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 force F is given by F =at + bt2 ,where, t istime. What are the dimensions of a and b ?
D.
Force F = at + bt2
From the principle of homogeneity
Dimension of at = dimension of F
The dimensional formula for Young's modulus is
[ML-1T-2]
[M0LT-2]
[MLT-2]
[ML2T-2]
A.
[ML-1T-2]
The formula for Young's modulus is
Y =
The length, breadth and thickness of ablock are given by l = 12 cm, b = 6 cm andt = 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 1in thickness, hence the volume will contain only onesignificant figure.
Therefore V= 2 ×102 cm3
In a system of units if force (F), acceleration (A),and time (T) are taken as fundamental units,then the dimensional formula of energy is:
FA2T
FAT2
F2AT
FAT
B.
FAT2
Let energy E = Fx Ay T3
Writing the dimensions on both sides
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
If C and R denote capacity and resistance, the dimensions of C R are :
M0L0T
ML0T
M0L0T2
not expressible in terms of M, L and T
A.
M0L0T
RC is the time constant of the circuit, so its dimensions are [M0L0T].
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
1.763 × 102 cm3
none of the above
B.
2 × 102 cm3
Using the relation for volume
V = length × breadth × thickness
= 12 × 6 × 2.45
= 176.4 cm
= 1.764 × 102 cm3
The minimum number of significant figures is 1 in breadth, hence, the volume will contain only one significant figure. Therefore,
V = 2× 102 cm3
The potential energy of a particle varies with distance x from a fixed origin as;where A and B are constants. The dimensions of AB are
D.