A screw gauge gives the following reading when used to measure the diameter of a wire.

        Main scale reading : 0 mm.

        Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is :

A spectrometer gives the following reading when used to measure the angle of a prism.

            Main scale reading        :   58.5 degree

            Vernier scale reading     :   09 divisions

Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data:

A student uses a simple pendulum of exactly 1m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 sec for this and records 40 seconds for 20 oscillations. For this observation, which of the following statement(s) is (are) true?

A Vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the Vernier scale which match with 16 main scale divisions. For this Vernier calipers, the least count is

To determine the half-life of the radioactive element, a student plots a graph of  $\mathrm{\ell n}\left|\frac{\mathrm{dN}\left(\mathrm{t}\right)}{\mathrm{dt}}\right|$ versus t. Here  $\frac{\mathrm{dN}\left(\mathrm{t}\right)}{\mathrm{dt}}$  is the rate of radioactive decay at time t. If the number of radioactive nuclei of this element decreases by a factor of p after 4.16 years, the value of p is