The given potentiometer has its wire of resistance 10$$\Omega$$. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2$$\Omega$$ resistor is :

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross-sections having radii r1 and r2 (r2 < r1). Choose the correct option as one moves from P to Q :

The resistance of a conductor at 15$${}^{\circ }$$C is 16$$\Omega$$ and at 100$${}^{\circ }$$C is 20$$\Omega$$. What will be the temperature coefficient of resistance of the conductor?

In the given figure, the emf of the cell is 2.2 V and if internal resistance is 0.6$$\Omega$$. Calculate the power dissipated in the whole circuit :

What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3$$\Omega$$ ? (Given resistivities of iron and copper-nickel alloy wire are 12 $$\mu$$$$\Omega$$ and 51 $$\mu$$$$\Omega$$ cm respectively)

If you are provided a set of resistances 2$$\Omega$$, 4$$\Omega$$, 6$$\Omega$$ and 8$$\Omega$$. Connect these resistances so as to obtain an equivalent resistance of {{46} \over 3}$$\Omega$$.

An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W.

Five identical cells each of internal resistance 1$$\Omega$$ and emf 5V are connected in series and in parallel with an external resistance 'R'. For what value of 'R', current in series and parallel combination will remain the same?

The Colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is :

For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be :

Consider a galvanometer shunted with 5$$\Omega$$ resistance and 2% of current passes through it. What is the resistance of the given galvanometer ?

The equivalent resistance of the given circuit between the terminals A and B is :

Due to cold weather a 1 m water pipe of cross-sectional area 1 cm2 is filled with ice at $$-$$10$${}^{\circ }$$C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 k$$\Omega$$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3.33 $$\times$$ 105 J kg$$-$$1, specific heat of ice = 2 $$\times$$ 103 J kg$$-$$1 and density of ice = 103 kg/m3

Two resistors R1 = (4 $$\pm$$ 0.8) $$\Omega$$ and R2 = (4 $$\pm$$ 0.4) $$\Omega$$ are connected in parallel. The equivalent resistance of their parallel combination will be :

A circular hole of radius \left( {{a \over 2}} \right) is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaining circular portion with respect to point 'O' will be :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body 'Q' having mass 'm' initially at rest. If m << M, body 'Q' will have a maximum speed equal to '2u' after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below :

Four equal masses, m each are placed at the comers of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be :

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is : (take g = 9.8 ms-2)

Two identical blocks A and B each of mass m resting on the smooth horizontal floor are connected by a light spring of natural length L and spring constant K. A third block C of mass m moving with a speed v along the line joining A and B collides with A. The maximum compression in the spring is

An object of mass m1 collides with another object of mass m2, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses m2 : m1 is :