Physics

Two metallic wires of identical dimensions are connected in series. If ${\sigma }_{1}and{\sigma }_2$ are the conductivities of these wires respectively, the effective conductivity of the combination is:

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\mathrm{\Delta }\mathrm{P}$ is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity $\mathrm{\Delta }T$ at constant pressure. The initial temperature and pressure of the gas were $300\mathrm{K}$ and 2 atm. respectively. If $\left|\mathrm{\Delta }T\right|=C\left|\mathrm{\Delta }P\right|$ then value of $C$  in (K/atm) is .

Given below are two statements.

Statement I : Electric potential is constant within and at the surface of each conductor.

Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

In the light of the above statements, choose the most appropriate answer from the options given below.

A spherically symmetric charge distribution is considered with charge density varying

as $\rho \left(r\right)=\{\begin{array}{cc}\hfill {\rho }_0\left(\frac{3}{4}-\frac{r}{R}\right)for\hfill & \hfill r\le R\hfill \\ \hfill zero\hfill & \hfill forr>R\hfill \end{array}$

Where, r(r < R) is the distance from the centre O (as shown in figure). The electric field at point P will be:

The distance between an object and a screen is $100\mathrm{c}\mathrm{m}$ . A lens can produce real image of the object on the screen for two different positions between the screen and the object.

The distance between these two positions is $40\mathrm{c}\mathrm{m}$ . If the power of the lens is close to $\left(\frac{\mathrm{N}}{100}\right)\mathrm{D}$ where $\mathrm{N}$ is an integer, the value of $\mathrm{N}$  is           

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination , is given by:

The speed verses time graph for a particle is shown in the figure. The distance travelled (in $\mathrm{m}$ ) by the particle during the time interval $\mathrm{t}=0$ to $\mathrm{t}=5\mathrm{s}$ will be $\dots .$ .

Given below are two statements : One is labeled as Assertion (A) and the other is labeled as Reason (R).

Assertion (A) : Clothes containing oil grease statins cannot be cleaned by water wash.

Reason (R) : Because the angle of contact between the oil/grease and water is obtuse.

In the light of the above statements, choose the correct answer from the option given below.

Two bodies of mass 1kg and 3kg have position vectors $\widehat{i}+2\widehat{j}+\widehat{k}and-3\widehat{i}-2\widehat{j}+\widehat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

A ball is projected with kinetic energy E, at an angle of 60° to the horizontal. The kinetic energy of this ball at the highest point of its flight will become: