Which of the following physical quantities have the same dimensions?

A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be:

The current I in the given circuit will be :

A battery of $$6\mathrm{V}$$ is connected to the circuit as shown below. The current I drawn from the battery is :

Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are $$r_1$$ and $$r_2$$ $$\left(r_1>r_2\right)$$. If the potential difference across the source of internal resistance $$r_1$$ is zero, then the value of R will be :

(A) The drift velocity of electrons decreases with the increase in the temperature of conductor. (B) The drift velocity is inversely proportional to the area of cross-section of given conductor. (C) The drift velocity does not depend on the applied potential difference to the conductor. (D) The drift velocity of electron is inversely proportional to the length of the conductor. (E) The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below :

A wire of resistance R1 is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is :

Given below are two statements : Statement I : A uniform wire of resistance $$80\Omega$$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $$5\Omega$$. Statement II: Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio $$3:2$$. In the light of the above statements, choose the most appropriate answer from the option given below

Two metallic wires of identical dimensions are connected in series. If $${\sigma }_1$$ and $${\sigma }_2$$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils. Reason R: Constantan and manganin have very small value of temperature coefficient of resistance. In the light of the above statements, choose the correct answer from the options given below.

A $$1\mathrm{m}$$ long wire is broken into two unequal parts $$\mathrm{X}$$ and $$\mathrm{Y}$$. The $$\mathrm{X}$$ part of the wire is streched into another wire W. Length of $$W$$ is twice the length of $$X$$ and the resistance of $$\mathrm{W}$$ is twice that of $$\mathrm{Y}$$. Find the ratio of length of $$\mathrm{X}$$ and $$\mathrm{Y}$$.

A body of mass M at rest explodes into three pieces, in the ratio of masses 1 : 1 : 2. Two smaller pieces fly off perpendicular to each other with velocities of 30 ms$$-$$1 and 40 ms$$-$$1 respectively. The velocity of the third piece will be :

Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates (0, 0) cm and (x, 0) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which the block of 30 kg must be moved to keep the position of centre of mass of the system unchanged is :

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

Two bodies A and B of masses 5 kg and 8 kg are moving such that the momentum of body B is twice that of the body A. The ratio of their kinetic energies will be :

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms$$-$$1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

A ball of mass $$0.15\mathrm{kg}$$ hits the wall with its initial speed of $$12{\mathrm{ms}}^{-1}$$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is $$100\mathrm{N}$$, calculate the time duration of the contact of ball with the wall.

A body of mass $$8\mathrm{kg}$$ and another of mass $$2\mathrm{kg}$$ are moving with equal kinetic energy. The ratio of their respective momentum will be :

A body of mass $$10\mathrm{kg}$$ is projected at an angle of $$45^{\circ }$$ with the horizontal. The trajectory of the body is observed to pass through a point $$(20,10)$$. If $$\mathrm{T}$$ is the time of flight, then its momentum vector, at time $$\mathrm{t}=\frac{\mathrm{T}}{\sqrt{2}}$$, is _____________. [Take $$\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$$ ]