Explore topic-wise InterviewSolutions in .

Three stars, each of mass $m$, are located at the vertices of an equilateral triangle of side $a$. They revolve in circular orbit under mutual gravitational force while preserving the equilateral triangle. Find the mechanical energy of the system.

The temperature, at which the root-mean-square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to :

[Boltzmann Constant $k_B=1.38\times {10}^{-23}\text{J/K}$

Avogadro Number $N_A=6.02\times {10}^{26}\text{/kg}$

Radius of Earth$:6.4\times {10}^6\text{m}$

Gravitational acceleration on Earth, $g=10{\text{ms}}^{-2}]$

If a simple pendulum has point of suspension at rest, the period of oscillation $T$ is related to length of the pendulum $l$ as:

A diatomic gas, having $C_p=\frac{7}{2}R$ and $C_v=\frac{5}{2}R$ is heated at constant pressure. The ratio $dU:dQ:dW$ is -

An uncharged sphere of metal is placed in a uniform electric field produced by two oppositely charged plates. The lines of force will appear as

The energy of an electrmagnetic radiation is $19.875\times {10}^{-13}erg$. What is the wave number in $c{m}^{-1}$? $h$ = $6.625\times {10}^{-27}erg.Sec$; $c$ = $3\times {10}^{10}cm.se{c}^{-1}$

Two similar coils of radius R are lying concentricaly with their planes at right angles to each other. The current flowing In them are l and 2l, respectively. The resultant magnetic field induction at the centre will be?

A monochromatic light of $\lambda =500A^{\circ }$ is incident on two identical slits separated by a distance of $5\times {10}^{-4}\text{m}$. The interference pattern is seen on a screen placed at a distance of $1\text{m}$ from the plane of slits. A thin glass plate of thickness $1.5\times {10}^{-6}\text{m}$ and refractive index $\mu =1.5$ is placed between one of the slits and the screen. Find the intensity at the center of the slit now.

The scale on a steel meter stick is calibrated at ${15}^{\circ }\text{C}$. Find the error in the reading of $60\text{cm}$ at ${27}^{\circ }\text{C}$. Given ${\alpha }_{\text{steel}}=1.2\times {10}^{-5}{}^{\circ }{\text{C}}^{-1}$

Object $A$ of mass $m$, is moving at a velocity $v_1$ to the right. It collides and sticks to object $B$ of mass $m_2$ moving in the same direction as object $A$ with velocity $v_2$. After collision, both the objects have the same velocity $\frac{1}{2}(v_1+v_2)$. What is the relationship between $m_1$ and $m_2$? [$v_1$ and $v_2$ are not equal]

Two rods $\text{A}$ and $\text{B}$ of different materials are welded together as shown in figure. Their thermal conductivities are $K_1$and $K_2.$ The thermal conductivity of the composite rod will be

An $AC$ voltage $E=220\sin (\omega t-\frac{\pi }{6})$ is connected across a certain device. The current flowing through this device is $i=115\sin (\omega t+\frac{\pi }{3})$. The correct phasor diagram, of applied voltage and current flowing in the circuit, is,

Due to some force $F_1$, a body oscillates with period $\frac{4}{5}\text{sec}$, and due to other force $F_2$, oscillates with period $\frac{3}{5}\text{sec}$. If both forces act simultaneously, the new period will be :

A particle is moving in a straight path with an acceleration $a=bn$, where $b$ is a positive constant $(n\ne -1)$. Assuming particle is at rest at origin at $t=0$, the relation between the velocity and the position$\left(r\right)$ of the particle at time $t=1\text{s}$ is



(Assume SI units)

A thick plano convex lens made of crown glass (refractive index 1.5) has a thickness of 3cm at its centre. The radius of curvature of its curved face is 5cm. An ink mark made at the centre of its plane face, when viewed normally through the curved face, appears to be at a distance 'x' from the curved face. Then, x is equal to:

A particle moves in a circle of radius 25 cm at two revolutions per sec. The acceleration of the particle in $m/s^2$ is :

If $\overrightarrow{a}=3\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{b}=4\hat{i}+3\hat{j}+4\hat{k},\overrightarrow{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}$ linearly dependent vectors and $|\overrightarrow{c}|=\sqrt{6},$ then the quadratic equation whose roots are $\alpha$ and $\beta$ can be

A small body of mass m can slide without friction along a trough bent which is in the form of a semi-circular arc of radius R. At what height h will the body be at rest with respect to the trough, if the trough rotates with uniform angular velocity $\omega$ about a vertical axis:

1. 50

When a particle is thrown in mud pond, it looses half of its speed after penetrating 3cm into mud. How much further it will penetrate before coming to rest ?(Assume that mud po nd offers uniform retardation)

If $\overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{C}$ , then which of the following statement is wrong?

1. 0.201

A projectile is fired with velocity $u$ making angle $\theta$ with the horizontal. What is the change in velocity when it is at the highest point

A block is projected with a velocity $20\text{m/s}$ up the incline plane of inclination angle ${60}^{\circ }$ and stops after $2\text{s}$. If $g=10{\text{m/s}}^2$, then the approximate value of coefficient of friction is