In order to determine the Young's Modulus of a wire of radius 0.2 cm (measured using a scale of least count = 0.001 cm) and length 1m (measured using a scale of least count = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1 g) was hanged to get the elongation of 0.5 cm (measured using a scale of least count 0.001 cm). What will be the fractional error in the value of Young's Modulus determined by this experiment?

One main scale division of a vernier callipers is 'a' cm and n^th division of the vernier scale coincide with (n $$-$$ 1)^th division of the main scale. The least count of the callipers in mm is :

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $$\lambda$$ where C/V = $$\lambda$$ ?

In a typical combustion engine the workdone by a gas molecule is given by $$W = {\alpha ^2}\beta {e^{{{ - \beta {x^2}} \over {kT}}}}$$, where x is the displacement, k is the Boltzmann constant and T is the temperature. If $$\alpha$$ and $$\beta$$ are constants, dimensions of $$\alpha$$ will be :