Explore topic-wise InterviewSolutions in .

An aeroplane is rising vertically with acceleration $f$. Two stones are dropped from it at an interval of time $t$. The distance between them at time $t^{\prime }$ after the second stone is dropped will be

A particle of mass $0.2\text{kg}$ is moving in one dimension under a force that delivers a constant power $0.5\text{W}$ to the particle. If the initial speed (in $\text{m/s})$ of the particle is zero, then speed in $\left(\text{m/s}\right)$ after $5\text{s}$ is

The position vector of four particles of masses $m_1=2\text{kg},m_2=4\text{kg},m_3=6\text{kg},m_4=8\text{kg}$ are $\overrightarrow{r_1}=2\hat{i}+3\hat{j}+0\hat{k},\overrightarrow{r_2}=0\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{r_3}=2\hat{i}+0\hat{j}+3\hat{k};\overrightarrow{r_4}=2\hat{i}+3\hat{j}+3\hat{k}$. The position vector of their centre of mass is given by

Find the derivative of the following function with respect to x. $y=\frac{sinx}{x}$

The equation for a wave travelling in $x$ direction on a string is given as

$y=10\sin (\pi t-0.5x)$, where $y$ and $x$ are in $\text{m}$ and time$\left(t\right)$ in $\text{sec}$. Find the acceleration of a particle at $x=\pi \text{m}$ at time $t=1\text{sec}$.

A body of mass $1kg$ is traveling with a velocity of $3m/s$ accelerates uniformly with $8m/s^2$ to travel for $2s$. Find its final momentum

A 30kg hammer strikes a steel spike (nail) 2.30 cm in diameter while moving with speed 20.0 m/s. The hammer rebounds with speed 10.0 m/s after 0.110s. The average strain in the spike during the impact will be

($Y=2\times {10}^{11}N/m^2$)

Water enters through end A with a speed v₁ and leaves through end B with a speed v₂ of a cylindrical tube AB. The tube is always completely filled with water. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward. We have v₁ = v₂ for

A body is projected horizontally with a velocity of $10\text{m/s}$ from the top of an inclined plane of angle ${45}^{\circ }.$ If the body hit the foot of the plane, the height of the plane (in $\text{m}$) is

The distance between a frog and an insect is $12\text{m}$ on a horizontal surface. The frog can jump with a maximum speed of $\sqrt{10}\text{m/s}$. The minimum number of jumps required by the frog to catch the insect is

$[$ Take $g=10{\text{m/s}}^2$ $]$

A solid cube floats in water half immersed and has small vertical oscillations of time period $\frac{\pi }{5}\text{s}$. Its mass $\left(\text{in kg}\right)$ is:

$(\text{Take}g=10{\text{ms}}^{-2})$

What is the equation of a sinusoidal wave moving in the positive x direction with wave length 6 m and time period 0.5s. The amplitude of the wave is 5 m.

A $1\text{m}$ long horizontal rope, having a mass of $40\text{g}$, is fixed at one end and is tied to a light string at the other end. The tension in the rope is $400\text{N}$. What will be the wavelengths (in $\text{metres}$) in the first and second overtone ?

If velocity of a particle is $v\left(t\right)=6-2t\text{m/s}$, the average speed and magnitude of average velocity of the particle in $5\text{sec}$ respectively are

What is the percentage change in length of 1m iron rod if the temperature change by ${100}^{\circ }$C ($\alpha =2\times {10}^{-5}{/}^{\circ }$)C

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are at right angles to each other , when

In a car lift, compressed air exerts a force $F_1$ on a small piston having a radius of $5.0\text{cm}$. This pressure is transmitted to the second piston of radius $10.0\text{cm}$. If the mass of the car to be lifted by the second piston is $1350\text{kg}$, calculate $F_1$ [Take $g=10{\text{m/s}}^2$]

Three capacitors are connected to DC source of 10volts shown in the

adjoining figure. If the charge accumulated on plates of C₁,C₂ and C₃ are

respectively, then

On an X temperature scale, water freezes at $-{125.0}^{\circ }$X and boils at ${375.0}^{\circ }$X. On a Y temperature scale, water freezes at $-{70.0}^{\circ }$Y and boils at $-{30.0}^{\circ }$Y. The value of temperature on X scale equal to the temperature of ${50.0}^{\circ }$Y on Y scale is:

A uniform bar of length 6a and mass 8 m lies on a smooth horizontal table. Two point masses m and 2m moving in the same horizontal plane with speed 2v and v respectively, strike the bar and stick to the bar after collision. Denoting angular velocity (about the centre of mass), total energy and centre of mass velocity by $\omega$, $E$ and $v_c$ respectively, we have after collision

A body is projected vertically upwards at time $t=0$ and it is seen at a height $H$ at times $t_1$ and $t_2$ seconds during its flight. The maximum height attained is ($g$ is the acceleration due to gravity)

The displacement is given by $x=2t^2+t+5$ in $\text{m}$, the acceleration at $t=5s$ will be

A sphere of mass M and radius R₂ has a concentric cavity of radius R_{1 as} shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the center of sphere varies as (0 $\le$ r $\le$ ∞)

A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is $T$. In a time $t=\frac{T}{6}$, the magnitude of average velocity of the particle is

A boy throws a ball upwards with velocity $v_0$ = 20 m/s . The wind imparts a horizontal acceleration of 4 m/$s^2$ to the left.

The angle $\theta$ at which the ball must be thrown so that the ball returns to the boy's hand is ( g = 10m/$s^2$ )

Find the tension $T_1$ in the string. All surfaces are smooth.

A square lamina is made up of a combination of $4$ smaller square plates. The density of plates are different and the whole arrangement is shown in the figure.





Find out the distance of $\text{COM}$ of given system from its geometric centre.

A ball rolls off the top of a stairway horizontally with a velocity of $4.5{\text{ms}}^{-1}$. Each step is $0.2\text{m}$ high and $0.3\text{m}$ wide. If $g$ is $10{\text{ms}}^{-2}$, then the ball will strike the $n^{th}$ step where $n$ is equal to

The potential energy (in SI units) of a particle of mass $2\text{kg}$ in a conservative field is $U=6x-8y$. If the initial velocity of the particle is $\overrightarrow{u}=-1.5\hat{i}+2\hat{j}\text{m/s},$ then the total distance travelled by the particle in first two seconds is

A bird is flying due east with a velocity of 4 m/s. The wind starts to blow with a velocity of 3 m/s due north. What is the magnitude of relative velocity of bird w.r.t. wind? Find out the angle it makes with the x-axis?

If the distance between the earth and the sun were half its present value, the number of days in a year would have been :

Find the ceff for this system having a variable dielectric

A soap bubble, having radius of $2\text{mm}$, is blown from a detergent solution having a surface tension of $5\times {10}^{-2}\text{N/m}$. Pressure inside the soap bubble is observed to be the same as the pressure at a point $h$ below the free surface of water taken in a container. Find the value of $h$.

[Take $g=10{\text{m/s}}^2$]

Three particles each of mass $2\text{kg}$ are placed at the corners of an equilateral triangle of side $6\text{m}$. What is the moment of inertia of the system about an axis passing through the height of the triangle on the same plane as the particles?

Three bodies of masses $1\text{kg}$, $3\text{kg}$ and $4\text{kg}$ have position vectors $(\hat{i}+2\hat{j}+\hat{k})$, $(-3\hat{i}-2\hat{j}+\hat{k})$ and $\left(4\hat{i}\right)$ respectively . The centre of mass of this system has position vector

In the arrangement shown, the acceleration of mass $2m$ is

The idea of secondary wavelets for the propagation of a wave was first given by

Two sound sources $S_1$ and $S_2$ emit pure sinusoidal waves in phase. If the speed of sound is $330\text{m/s}$, then for what frequencies does constructive interference occur at P?

What is the mutual inductance of a two-loop system as shown with centre separation l

What will the value of angular magnification be if the final image is formed at near point, instead of infinity?

When a moving bus stops immediately , you feel a push forward. Who pushed you?

If $W_1,W_{2}and{W}_3$ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation