Units and Measurements

Consider the equation H= xp qErts Where H = magnetic field intensity; E = electric field, = permittivity, x = distance, t = time The values of p, q, r and s respectively are :

1. 1, 1, 1, 1
2. -1, 1, 2, 1
3. 1, -1, -2, 1
4. -1, -2, -2, 1

The potential energy of a particle changes with distance x from a fixed origin as V= A xx+B, where A and B are constants with appropriate dimensions. The dimensions of AB are .

1. [ M1L5/2T-2]
2. [ M3/2L5/2T-2]
3. [ M1L2T-2]
4. [ M1L7/2T-2]

Consider a modified Bernoulli equation. (P + ABt2 ) + g(h + Bt) + 12 V2 = constant If t has the dimension of time then the dimensions of A and B are , respectively.

1. [ ML0T-1] and [M0LT]
2. [ ML0T-2] and [ M0LT-1]
3. [ ML0T-2] and [ M0LT-2]
4. [ ML0T-1] and [ M0LT-1]

The expression given below shows the variation of velocity (v) with time (t), v = At2 + BtC + t. The dimension of ABC is :

1. [ M0L1T-2]
2. [ M0L2T-3]
3. [ M0L2T-2]
4. [ M0L1T-3]

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

1. E2=pc2+m2c4
2. E2=pc2+m2c2
3. E2=p2c2+m2c4
4. E2=p2c2+m2c2

The position of a particle moving on x-axis is given by x(t)=A t+B 2t+Ct2+D, where t is time. The dimension of ABCD is

1. L
2. L3 T-2
3. L2 T-2
4. L2

The electric flux is = + where and are linear and surface charge density, respectively. ( ) represents

1. displacement
2. charge
3. electric field
4. area

The equation of stationary wave is : y=2a ( 2 ) ( 2 x ). Which of the following is NOT correct :

1. The dimensions of nt is [L]
2. The dimensions of n is [ LT-1]
3. The dimensions of x is [L]
4. The dimensions of n/ is [T]

Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

1. T2 = 4 2 rGM2
2. T2 = 4 2 r3
3. T2 = 4 2 r3GM
4. T2 = 4 2 r2GM

A force is represented by F=ax2+bt 12 where x= distance and t= time. The dimensions of b2/a are:

1. [ ML2 T-3 ]
2. [ ML3 T-3 ]
3. [ MLT-2 ]
4. [ ML-1T-1 ]

Consider two physical quantities A and B related to each other as E= B-x2At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

1. L-2M1T0
2. L2M-1T1
3. L0M-1T1
4. L-2M-1T1

If mass is written as m=kcPG-1/2h1/2 then the value of P will be : (Constants have their usual meaning with k a dimensionless constant)

1. 1/3
2. -1/3
3. 1/2
4. 2