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The metallic bob of a simple pendulum has the relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then the new time period is given by

Potentiometer wire of length $10\text{m}$, having a total resistance of $10\Omega$. A battery of emf $2\text{V}$ of negligible internal resistance and a rheostat are connected to it. If the potential gradient is $20\text{mV/m}$, find the resistance of the rheostat.

The value of $\underset{0}{\overset{\frac{\pi }{2}}{\int }}{\sin }^6\left(x\right)dx$ is:

Two strings are tied $2\text{m}$ apart on a rod and on the other end a mass $200\text{g}$ is tied as shown in figure. Each string is $1.25\text{m}$ long. FInd the tensions $T_1$ and $T_2$ if the rod is rotated with $60\text{rpm}$. Consider ${\pi }^2=10$

Metallic sphere of radius $5cm$ is surrounded by air. Dielectric strength of air is $5\times {10}^{5}V/m$ , then maximum charge that can be placed on sphere is

The displacement of tip of the second hand of an analog watch when it turns for $15\text{sec}$ is

A spherically symmetric gravitational system of particles has a mass density,

$\rho =\{\begin{array}{c}{\rho }_0\text{for}r\le R_0\\ 0\text{for}r>R\end{array}$

where ${\rho }_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $v$ as a function of distance $r(0<r<\infty )$ from the centre of the system is represented by-

The condition for a body having density ${\rho }_b$ to float completely immersed in the liquid having density ${\rho }_L$ is

When a spiral spring is stretched by suspending a load on it, the strain produced is called

The current flowing in $3\Omega$ resistance will be

1. 7.64

Magnetic field due to two current carrying conductors of the same length at the same point is $B$ and $\frac{B}{4}$ respectively when they are placed near the point one after the other. Now, if the direction of current of the first conductor is reversed, then the value of respective magnetic fields will be:



$($Here, negative sign represents the reversal of direction of the magnetic field$)$

A particle is moving along the x-axis under the influence of a force given by F = –5x + 15. At time t = 0 the particle is located at x = 6 and is having zero velocity. It takes 0.5 seconds to reach the origin for the first time. The equation of motion of the particle can be represented by

Question 1

What are the differences between the mass of an object and its weight?

What do you mean by electroplating? Explain.

When two capacitors C₁ and C₂ are connected in series and parallel, their equivalent capacitances comes out to be 3 μF and 16 μFrespectively. Calculate values of C₁ and C₂.

A uniform solid sphere of radius $R$ and mass $m$ rolls down an inclined plane. The coefficient of friction between the sphere and the inclined plane is $\mu$ then maximum value of $\theta$ for pure rolling is

A proton and an $\alpha$ - particle accelerated through the same potential difference enter a region of uniform magnet field normally. If the radius of proton orbit is 10 cm then radius of $\alpha$ - particle orbit is

The value of $100+0.40$ with regards of significant figure will be

A rigid body of mass M and radius R rolls without slipping on an inclined plane of inclination $\theta$, under gravity. Match the type of body with magnitude of the force of friction.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(a)}& \text{For ring}& \text{(p)}& \frac{Mgsin\theta }{2.5}\\ \text{(b)}& \text{For solid sphere}& \text{(q)}& \frac{Mgsin\theta }{3}\\ \text{(c)}& \text{For solid cylinder}& \text{(r)}& \frac{Mgsin\theta }{3.5}\\ \text{(d)}& \text{For hollow spherical shell}& \text{(s)}& \frac{Mgsin\theta }{2}\end{array}$

If we don't want an induced e.m.f. in a coil kept in uniform magnetic field. We should

If the speed of a car is given as $v=3t^2+2t\text{m/s}$, the average speed in $10sec$ is

A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of $2\text{V}$ and a negligible internal resistance. The potentiometer wire itself is $4\text{m}$ long. When the resistance $R$ is connected across the given cell has value of $\left(i\right)$ infinity, $\left(ii\right)9.5\Omega$ the balancing length on the potentiometer wire are found to be $3\text{m}$ and $2.85\text{m}$ respectively. The value of internal resistance of the cell is

Inside a physics lab: (vibrating tuning fork does SHM)

Teacher: this experiment is about finding the frequency of oscillation of different tuning forks.

You hit it against something and take it close to this device [pointing at the device] which measures the frequency. The oscillation of a tuning fork is simple harmonic.

Student X hits a thick tuning fork lightly and finds out its frequency as f. student x then hits a thin one lightly and finds its frequency to be f'. student x thinks if he hit the thick one hard enough its frequency might come out to be f'. The student tries this.

Four particles each having a charge $q$ are placed on the four vertices of a regular pentagon. The distance of each corner from the centre is $a$. Find the electric field at the centre of the pentagon.

A series R-L-C circuit has a Q of 100 and an impedance of (100 + j0) $\Omega$ at its resonant angular frquency of

${10}^7$ radians/sec. The values of R and L are:

R = L=

The radii of two planets are respectively $R_1$ and $R_2$, and their densities are respectively ${\rho }_1$ and ${\rho }_2$. The ratio of the acceleration due to gravity at their surface is