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

                   

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	0.01 mm	5 mm

Then the fractional error in the measurement of Y is:

A wire of length 'l' and resistance $100\Omega$  is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:

A thin spherical shell is charged by some source. The potential difference between the two points $C$ and $P$  (in V) shown in the figure is:

(Take  $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9$  SI units)

A uniform heating wire of resistance 36 $\Omega$  is connected across a potential difference of 240V. The wire is then cut into half and a potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : x, where x is________.

The terminal voltage of the battery, whose emf is 10 V and internal resistance $1\Omega$ , when connected through an external resistance of $4\Omega$  as shown in the figure is:

A current of 5A is passing through a non-linear magnesium wire of cross – section 0.04m². At every point the direction of current density is at an angle of 60° ;with unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (Resistivity of magnesium $\rho =44\times 10^{-8}\Omega m)$ <!-- [if gte mso 9]><xml> </xml><![endif]-->