Explore topic-wise InterviewSolutions in .

The position $x$ of a moving particle at time $t$ is given by $x=t^2+2t+3\text{m}$. The average velocity of the particle during the first second of its motion is

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $\frac{g}{8}$, then the ratio of the masses is

The water equivalent of $20\text{g}$ of aluminium (specific heat $0.2{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$) , is

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L(L>>l)$. The loops are co-planar and their centers coincide. The mutual inductance of the system is proportional to

In figure, a light ray refracts from material $1$ into a thin layer of material $2$, crosses that layer, and then is incident at the critical angle on the interface between materials $2$ and $3$. The angle $\theta$ is

Three charges $-Q,q$ and $-3Q$ are arranged as shown in figure. The system of charges will have positive configuration energy if

The speed of a car as a function of time is shown in figure. Find the distance travelled by the car in 8 seconds and its acceleration.

A projectile of mass $0.5\text{kg}$ is thrown with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ with the horizontal. Find the net force acting on the body when in air. (Take $g=9.8m/s^2$)

A cyclist bends while taking a sharp turn so that

The radii of curvature of a lens are + 20 cm and + 30 cm. The material of the lens has a refracting index 1.6. Find the focal length of the lens

(a) If it is placed in air, and

(b) If it is placed in water $(\mu =1.33)$.

How to find after rubbing which all particles will have positive charges and which all will have negative charges while such questions are given in exams?

Nb: Without electroscope.

The two nearest harmonics of a tube closed at one end and open at other end are $220Hz$ and $260Hz$. What is the fundamental frequency of the system?

In the given R – C circuit switch S is closed at t = 0 and the variation of potential drop across the resistor $\left(V_R\right)$ and across capacitor $\left(V_C\right)$ is represented by given plot, then :

Three uniform rings made of the same material are arranged co-axially to form a system and the radii of the rings are $r_1=3\text{m},r_2=2\text{m}$ and $r_3=1\text{m}$. Find the $y-$ coordinate of $\text{COM}$ of the system.

The solution of the curve given by $y\sin x=\underset{0}{\overset{x}{\int }}t\sin tdt,x\in (0,\frac{\pi }{2})$ and $y\left(\frac{\pi }{2}\right)=1,$ is

A large open tank has two holes in the wall. One is a square hole of side $L$ at a depth $y$ from the top, and the other is a circular hole of radius $R$ at a depth $4y$ from the top. When the tank is completely filled with water, the quantities of water flowing out per $\text{second}$ from holes are the same. Then $R$ is equal to

An optical device is constructed by fixing three identical convex lenses of focal lengths 10 cm each inside a hollow tube at equal spacing of 30 cm each. One end of the device is placed 10 cm away from a point source. How much does the image shift when the device is moved away from the source by another 10 cm?

Two elastic rods are joined between fixed supports as shown in figure. Condition for no change in the lengths of the individual rods with increase in temperature -

[Given $\alpha \to$ linear expansion coefficient, $A\to$ area of cross-section of rod, $Y\to$ Young's modulus and $L\to$ length of rod]

When the gap is closed without placing any object in the screw gauge whose least count is $0.005\text{mm}$, the $5^{th}$ division on its circular scale coincides with the reference line on main scale. When a small sphere is placed, the reading on the main scale advances by 4 divisions, whereas the ${25}^{th}$ division on its circular scale coincides with the reference line on the main scale. There are 200 divisions on the circular scale. The radius of the sphere measured is