If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimension of the radius of gyration is 

(1) $h^{1/2}{c}^{-3/2}{G}^{1/2}$

(2) $h^{1/2}{c}^{3/2}{G}^{1/2}$

(3) $h^{1/2}{c}^{-3/2}{G}^{-1/2}$

(4) $h^{-1/2}{c}^{-3/2}{G}^{1/2}$

X = 3YZ² find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively

(1) $M^{-3}{L}^{-2}{T}^{-4}{A}^{-1}$

(2) ML^–2

(3) $M^{-3}{L}^{-2}{T}^4{A}^4$

(4) $M^{-3}{L}^{-2}{T}^8{A}^4$

In the relation $P=\frac{\alpha }{\beta }{e}^{-\frac{\alpha Z}{k\theta }}$, P is pressure, Z is the distance, k is the Boltzmann constant and θ is the temperature. The dimensional formula of β will be:

(1) $\left[M^0{L}^2{T}^0\right]$

(2) $\left[M^1{L}^2{T}^1\right]$

(3) $\left[M^1{L}^0{T}^{-1}\right]$

(4) $\left[M^0{L}^2{T}^{-1}\right]$

The frequency of vibration of string is given by $\nu =\frac{p}{2l}{\left[\frac{F}{m}\right]}^{1/2}$. Here p is number of segments in the string and l is the length. The dimensional formula for m will be

(1) $\left[M^{0}L{T}^{-1}\right]$

(2) $\left[M{L}^0{T}^{-1}\right]$

(3) $\left[M{L}^{-1}{T}^0\right]$

(4) $\left[M^0{L}^0{T}^0\right]$

Choose the correct match 

(1) (i) G, (ii) H, (iii) I, (iv) B, (v) C

(2) (i) D, (ii) H, (iii) I, (iv) B, (v) G

(3) (i) G, (ii) H, (iii) I, (iv) B, (v) G

(4) None of the above

A wire has a mass of \((0.3\pm0.003)\) grams, a radius of \((0.5\pm 0.005)\) mm, and a length of \((0.6\pm0.006)\) cm. The maximum percentage error in the measurement of its density will be:
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)

If \(97.52\) is divided by \(2.54\), the correct result in terms of significant figures is:

Assertion : ‘Light year’ and ‘Wavelength’ both measure distance.

Reason : Both have dimensions of time.

Assertion : Light year and year, both measure time.

Reason : Because light year is the time that light takes to reach the earth from the sun.

Assertion : Force cannot be added to pressure.

Reason : Because their dimensions are different.