A student determined Young's Modulus of elasticity using the formula $$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The value of g is taken to be 9.8 m/s², without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression ($$\delta $$)	0.01 mm	5 mm

Then the fractional error in the measurement of Y is :

If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :

Match List - I with List - II.

	List - I		List - II
(a)	Torque	(i)	MLT$$^{ - 1}$$
(b)	Impulse	(ii)	MT$$^{ - 2}$$
(c)	Tension	(iii)	ML$$^{ 2}$$T$$^{ - 2}$$
(d)	Surface Tension	(iv)	MLT$$^{ - 2}$$

Choose the most appropriate answer from the option given below :

Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension, $$\theta$$ = angle, $$\rho$$ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T = torque, $$\in$$ = permittivity, E = electric field, J = current density, L = length.