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A wire suspended vertically from one of its ends is stretched by attaching a weight of $200\text{N}$ to its lower end. If the weight stretches the wire by $1\text{mm}$, then elastic energy stored in the wire is

If a gas has ${}^{\prime }{f}^{\prime }$ degree of freedom, the ratio of specific heats of the gas $\left(\frac{C_P}{C_V}\right)$ is

When water $(\text{viscosity,}{\eta }_w=0.01\text{poise})$ and benzene $(\text{viscosity,}{\eta }_b=0.0065\text{poise})$ are allowed to flow through a pipe, it was found that the same amount of liquids are collected in the same time but the pressure drop that caused the flow are different. If the pressure drop in water is $0.015\text{atm}$, then the pressure drop in benzene will be

When a potential difference is applied across, the current passing through

If the $10\text{kg}$ and $20\text{kg}$ bodies are considered to be system $1$ and $30\text{kg}$ body is considered as system $2$ , how many forces would appear to be acting as external forces for system $1$?

The apparent frequency of the whistle of an engine changes in the ratio of 6:5 as the engine passes a stationary observer. If the velocity of sound is 330 m/s, then the velocity of the engine is

A uniform circular disc of radius 'R' with a concentric circular hole of radius $\frac{R}{2}$ rolls on a horizontal plane. The fraction of its total energy associated with its rotational motion is

When the ratio of the minimum velocity to the maximum velocity is $\frac{1}{\sqrt{2}}$ in a projectile motion, the angle of projection of projectile is

An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is 3.6 × ${10}^{-5}{/}^{\circ }C$ )

In the arrangement shown in figure, pulleys are fixed and the ends $P$ and $Q$ of an unstretchable string move downwards with a uniform speed $u$. Mass $m$ moves upwards with a speed of

How many significant figures are there in the product:

$(2.156\times {10}^1)\times (4.567891\times {10}^2)\times (5.1102\times {10}^3)$

The displacement of a body in $8s$ starting from rest with an acceleration of $20{\text{cm/s}}^2$ is

The dimensional formula of mobility of holes or electrons in diode is

If error in measurement of radius of sphere is $1\%$, what will be the error in measurement of volume?

Difference in height of the liquid columns in the limbs of a rotating $U-$ tube as shown in the figure is:

(Neglect the width of each limb and take $g=10{\text{m/s}}^2$)

From a solid sphere of mass $M$ and radius $R$, a spherical portion of radius $\left(\frac{R}{2}\right)$ is removed as shown in the figure. Taking gravitational potential $V=0$ at $r=\infty$, the potential at the centre of the cavity thus formed is (G = gravitational constant)

A man is $180\text{cm}$ tall and his eyes are $10\text{cm}$ below the top of his head. In order to see this entire height right from toe to head, he uses a plane mirror kept at a distance of $1\text{m}$ from him. The minimum length of the plane mirror is

In which of the following cases is the contact force between $A$ and $B$ is maximum. If mass of each block is $1\text{kg}$ and assume all surfaces to be smooth :-

Span of a bridge at ${10}^{\circ }\text{C}$ is $2.4\text{km}$ long. At $30{}^{\circ }\text{C}$, the cable along the span sags by $0.5\text{km}$. Change in length of the cable when temperature changes from ${10}^{\circ }\text{C}$ to ${42}^{\circ }\text{C}$ is

$[\alpha =12\times {10}^{-6}/{}^{\circ }\text{C}]$

A string can sustain a maximum force of $200\text{N}$ without breaking. A block of mass of $1\text{kg}$ is tied to one end of the string of $2\text{m}$ long and the mass is rotated in a horizontal circular path. The maximum linear speed of mass is (in $\text{m/s}$).

A stone weighing $3kg$ falls from the top of a tower $100m$ high and buries itself $2m$ deep in sand. Find the time (in seconds) of penetration $(g=10m/s^2)$

A particle of mass 0.01 kg travels along a curve with velocity given by $4\hat{i}+16\hat{k}m{s}^{-1}$. After some time, its velocity becomes $8\hat{i}+20\hat{j}m{s}^{-1}$ due to the action of a conservative force. The work done on particle during this interval of time is

In a horizontal pipeline of variable cross-section, $2\times {10}^{-2}\text{J/kg}$ is the change in kinetic energy per $\text{kg}$ of the kerosene oil flowing through the pipe of length $1500\text{m}$. What will be the pressure drop between the end points of the pipe? (Take density of kerosene oil as $850{\text{kg/m}}^3)$

Find the area enclosed by the curve $y=x^2$ and the x-axis for interval x = 1 to x = 3.

A bullet of mass m leaves a gun of mass M kept on a smooth horizontal surface. If speed of the bullet relative to the gun is v, then recoil speed of the gun will be:

A sample of $0.1g$ of water at $100°C$ and normal pressure ($1.013\times {10}^{5}N{m}^{–2}$) requires $54cal$ of heat energy to convert to steam at $100°C$. If the volume of the steam produced is $167.1c\mathrm{c,}$ the change in internal energy of the sample is

A photo cell is receiving light from a source placed at a distance of 1 m. If the same source is to be placed at a distance of 2 m, then the ejected electron

An aluminium sphere of $20\text{cm}$ diameter is heated from $0^{\circ }C$ to ${100}^{\circ }C$. Its volume changes by (given that coefficient of linear expansion for aluminium ${\alpha }_{Al}=23\times {10}^{-6}{/}^{\circ }C$

A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$ . After some time the velocity of the ball attains a constant value known as terminal velocity $v_r$. The terminal velocity depends on $\left(i\right)$ the mass of the ball $m,\left(ii\right)\eta ,\left(iii\right)rand\left(iv\right)$ acceleration due to gravity $g$ . Which of the following relations is dimensionally correct

Angular momentum is

A hollow spherical ball of radius $2\text{m}$ and mass $3\text{kg}$ is rotating about a fixed axis passing through its COM. If it has kinetic energy of $576\text{J}$, the angular speed of the hollow spherical ball about the fixed axis is

Three identical rods of length $1\text{m}$ each, having cross-sectional area of $1{\text{cm}}^2$ each and made of aluminium, copper and steel respectively are maintained at temperatures of ${12}^{\circ }\text{C},4^{\circ }\text{C}$ and ${50}^{\circ }\text{C}$ respectively at their separate ends. Find the temperature of their common junction.

$[K_{Cu}=400\text{W/m-K},K_{Al}=200\text{W/m-K},K_{\text{Steel}}=50\text{W/m-K}]$

Consider six wires carrying same current coming into or out of the page. Rank the line integral of the magnetic field (from most positive to most negative) taken counter-clockwise around each loop shown.

Rajat is sitting in an open cart that moves horizontally with an acceleration of $5m/s^2$ rightwards. Rajat is unaware of his acceleration, and throws a ball up in the air. He attempts at drawing a Free Body Diagram of the ball assuming his frame to be inertial. Which of these would closely resemble his free body diagram of the ball (neglect air drag)?

The normal reaction between the blocks $N_1,N_2$ are

Two point charges A and B having charges $+q$ and $–q$ respectively are placed at certain distance apart and force acting between them is $F$. If 25% charge of A is transferred to B, force between the charges becomes

A particle has the position vector $\overrightarrow{r}=\hat{i}-2\hat{j}+\hat{k}$ and the linear momentum $\overrightarrow{p}=2\hat{i}-\hat{j}+\hat{k}$. Then, its angular momentum about the origin is

Four particles each of mass $500\text{g}$ are placed at the four corners of a rectangle $ABCD$ with sides of length $5\text{m}$ and $10\text{m}$. What is the ratio of moment of inertia of the system when $AB$ is the axis to when $BC$ is the axis?

Which of the given relations about the above elements are correct.

I) ${}^{12}C$

II) ${}^{14}C$

III) ${}^{14}N$

IV) ${}^{16}O$

A monkey hangs on a rope. The rope goes up over a pulley, and on the other end is an equal weight of block filled with bananas. Now the monkey starts climbing up the rope. What can be the possible cases as observed by a boy on the ground?

Two masses $m_1$ and $m_2$ are moving with velocities $v_1$ and $v_2$ respectively. Find their total kinetic energy in the reference frame of centre of mass.

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area $A$ and the second wire has cross-sectional area $3A$. If length of the first wire is increased by $\Delta l$ on applying a force $F$, then how much force is needed to stretch the second wire by the same amount?

A person walking at $3\text{kmph}$ finds rain falling vertically. When he walks in the opposite direction with the same speed, the rain appears to fall at ${45}^{\circ }$ to the vertical. What is the speed of rain ?

Two particles are in SHM in a straight line about same equilibrium position. Amplitude $A$ and time period $T$ of both the particles are equal. At time $t=0$, one particle is at displacement $y_1=+A$ and the other at $y_2=-\frac{A}{2}$, and they are approaching towards each other. After what time they cross each other?

The following figure shows a network of currents, their magnitudes and directions. The current $I$ will be equal to _____.