Explore topic-wise InterviewSolutions in .

A metal rod of length $50\text{cm}$ having mass $2\text{kg}$ is supported on two edges placed $10\text{cm}$ from each end. A $3\text{kg}$ load is suspended at $20\text{cm}$ from one end. Find the reactions at the edges (take $g=10{\text{m/s}}^2$)

Two vectors acting in the opposite directions have a resultant of 10 units. If they act at right angles to each other, then the resultant is 50 units. Calculate the magnitude of two vectors.

A space shuttle moving at $2\text{m/s}$ at $t=0$ begins to accelerate at a constant rate of $2{\text{m/s}}^2$. If $S_n$ is the distance covered by it in the ${\text{n}}^{\text{th}}$ second, then:

$y=\frac{sinx}{x+cosx},then\frac{dy}{dx}=?$

In the figure below, $10\text{mC}$ charge is fixed. A $50\mu \text{C}$ charge having mass $10\text{g}$ is projected from infinity towards the $10\text{mC}$ charge. Calculate initial velocity of projection if minimum distance between the charges is $10\text{cm}$.

Potential energy $U\left(x\right)$ and associated force $F\left(x\right)$ bear the relation $F\left(x\right)=\frac{-dU\left(x\right)}{dx}$. Dependence of potential energy of a two-particle system on the separation $x$ between them is shown in the following figure.





Which of the following graphs shows the correct variation of force $F\left(x\right)$ with $x$?

A motorcyclist of mass $100\text{kg}$ is moving in a horizontal circle inside a hollow cylinder of radius $50\text{m}$. The coefficient of friction between the tires of the motorcycle and the surface of the hollow cylinder is $0.8$. Then, the minimum speed with which he should ride the motorcycle to keep moving in a horizontal circle is

A planet moves around the sun. At a given point P, it is closest from the sun at a distance $d_1$ and has a speed $v_1$. At another point Q, when it is farthest from the sun at a distance $d_2$, its speed will be

Figure shows the temperature variation when heat is added continuously to a specimen of ice $\left(10\text{g}\right)$ at $-{40}^{\circ }\text{C}$ at constant rate. (Specific heat of ice $=0.53{\text{cal/g}}^{\circ }\text{C}$ and $L_{\text{ice}}=80\text{cal/g},L_{\text{water}}=540\text{cal/g)}$



$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \left(A\right)\text{Value of}{Q}_1\text{(in cal)}& \left(P\right)800\\ \left(B\right)\text{Value of}{Q}_2\text{(in cal)}& \left(Q\right)1000\\ \left(C\right)\text{Value of}{Q}_3\text{(in cal)}& \left(R\right)5400\\ \left(D\right)\text{Value of}{Q}_4\text{(in cal)}& \left(S\right)212\\ & \left(T\right)900\end{array}$

Find the unit vector in the direction opposite to the direction of the vector $6\hat{i}-8\hat{j}+10\hat{k}$

A thin lens has focal length f and aperture radius r. It forms an image of intensity I. Now the central part of the aperture upto $\frac{r}{2}$ is blacked by an opaque material. The focal length and intensity of image will be

The graph shows a wave at t = 0 travelling to the right with a velocity of 4 m/s. The equation that best represents the wave is

Which of the following represents an infrared wavelength

When shearing force is applied on a body, then the elastic potential energy is stored in it. On removing the force, this energy is most likely to get converted into

The bob of a pendulum is released from a horizontal position A as shown in the figure. The length of the pendulum is 2 m. If $10\%$ of the initial energy of the bob is dissipated as heat due to the friction of air, what would be the speed of the bob when it reaches the lowermost point B? Take $g=10m{s}^{-2}$.

Three masses of 15 kg. 10 kg and 5 kg are suspended vertically as shown in the fig. If the string attached to the support breaks and the system falls freely, what will be the tension in the string between 10 kg and 5 kg masses. Take $g=10m{s}^{-2}$ . It is assumed that the string remains tight during the motion

Find the force of interaction between the $2kg$ and $1kg$ bodies.

Photoelectric effect experiments are performed using three different metal plates p,q and r having work functions ${\varphi }_p=2.0eV,{\varphi }_q=2.5eVand{\varphi }_r=3.0eV$, respectively. A light beam containing wavelengths of 550 nm, 450 nm and 350 nm with equal intensties illuminates each of the plates. The correct I-V graph for the experiment is (IIT-JEE-2009)

A particle of mass $2\text{kg}$ moving with a velocity of $3\text{m/s}$ is acted upon by a force which changes its direction of motion by an angle of ${90}^{\circ }$ without changing its speed. What is the magnitude of impulse experienced by the particle?

A uniform ball of radius $r$ rolls without slipping down from the top of a sphere of radius $R$. The angular velocity of the ball when it breaks from the sphere is

A circular disc of radius R has a uniform thickness. A circular hole of diameter equal to the radius of the disc has been cut out as shown in figure. Find the centre of mass of the remaining disc.

The beta particle consists of

A stone $A$ is dropped from rest from height $h$ above ground. A second stone $B$ is simultaneously thrown vertically up with velocity $v$. Find $v$ so that $B$ meets midway between their initial positions.

Liquid rises to a height of $2\text{cm}$ in a capillary tube. The angle of contact between the solid and the liquid is zero. The tube is depressed more now so that the top of the capillary is only $1\text{cm}$ above the liquid. Then, the apparent angle of contact between the solid and the liquid is:

An ac voltage is represented by $E=220\sqrt{2}cos\left(50\pi \right)t$ How many times will the current becomes zero in 1 s?

A soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces constant increase in the radius per minute of the bubble, irrespective of its internal pressure. The graph between the excess pressure $p$ inside the soap bubble and time $t$ will be

A body is moving from rest under constant acceleration and let $S_1$ be the displacement in the first $(p–1)\text{sec}$ and $S_2$ be the displacement in the first $p\text{sec}$. The displacement in $(p^2–p+1{)}^{\text{th}}\text{sec}$ will be

The Lyman series of hydrogen spectrum lies in the region of

A solid cone of height $2R$ and base radius $R$ is placed over a solid hemisphere as shown in figure. Cone and hemisphere are made up of the same material. Height of center of mass of system from the ground is

Masses $8\text{kg}$, $2\text{kg}$ , $4\text{kg}$ & $2\text{kg}$ are placed at the corners $\text{A, B, C, D}$ respectively of a square $\text{ABCD}$ of diagonal $80\text{cm}$ (as shown in the figure below). The distance of the centre of mass from $A$ will be

Consider the general motion of a wheel of radius $2\text{m}$ which can be viewed as pure translation with the velocity $\overrightarrow{v}$ and pure rotation about $\text{O}$ with angular velocity $5\text{rad/s}$. Which of the following is incorrect?

A pulley-block system is as shown in the figure. Blocks $2\text{kg}$ and $3\text{kg}$ are at rest. Coefficient of friction between $2\text{kg}$ and incline is

The period of a satellite in a circular orbit of radius R is T, the period of another satellite in a circular orbit of radius 4R is

If mercury is replaced with water in barometer, what would be the height of water column at standard atmospheric pressure, i.e., $76cm$ of mercury? (Specific gravity of mercury $=13.6$)

When fluids of density $2.2\text{g/cc}\&4.8\text{g/cc}$ are mixed together in equal volumes, then the density of the resulting mixture will be

Consider the figure. Each capacitor has capacitance C.

The equivalent capacitance between 4 and 5 is

The Bat Life: Batman is undercover, and to prevent anyone from recognizing his voice (or Bruce Wayne's) he inhales a very dilute Helium gas (search YouTube for "voice after helium” to see the effects). The helium is stored ina cylindrical chamber as shown.

During a fight one of the steel balls gets dislodged. What will happen to the piston?

Two spheres of equal masses are attached to a string of length $2\text{m}$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant rate. What is the value of the ratio

$\left(\frac{\text{Tension in the string between}P\text{and}Q}{\text{Tension in the string between}P\text{and}O}\right)$?

A circuit contains two inductors of self-inductance $L_1$ and $L_2$ in series (see figure). If $M$ is the mutual inductance, then the effective inductance of the circuit shown will be

A uniform rod of length $l$ is acted upon by a force $F$ in a gravity free region, as shown in the figure. If the area of cross-section of the rod is $A$ and its Young's modulus is $Y$, then the elastic potential energy stored in the rod due to elongation is

A bomb is dropped on an enemy post by an aeroplane flying horizontally with a velocity of $60{\text{kmh}}^{-1}$ and at a height of $490\text{m}$. At the time of dropping the bomb, how far the aeroplane should be from the enemy post so that the bomb may directly hit the target?

A small mass m is attached to a massless string whose other end is fixed at p as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at 0 and constant angular speed $\omega$. If the angular momentum of the system, calculated about o and p are denoted by $L_{o}and{L}_p$ respectively, then

Calculate the magnitude of work done when 4 moles of a perfect gas are compressed adiabatically. The initial pressure and volume of the gas are ${10}^5{\text{N/m}}^2$ and 8 litres respectively. The final volume of the gas is 4 litres. Molar specific heat of the gas at constant volume is $3R/2$.

If $\overrightarrow{a}=\hat{i}-\hat{j}$ and$\overrightarrow{b}=3\hat{i}+4\hat{j}$, the vector having the same magnitude as $\overrightarrow{b}$ and parallel to $\overrightarrow{a}$ is

A constant force $F$ acts tangentially at the highest point of a uniform disc of mass $m$ kept on a rough horizontal surface as shown in figure. If the disc rolls without slipping, calculate the acceleration of the centre $C$ and points $A$ and $B$ on the disc.