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An ice cube contains a glass ball. The cube is floating on the surface of water contained in a trough. What will happen to the water level, when the cube melts?

Trajectory of two particles projected from origin with speeds $v_1$ and $v_2$ at angles ${\theta }_1$ and ${\theta }_2$ with positive x-axis respectively are as shown in the figure. Given that $g=-10{\text{m/s}}^2\left(\hat{j}\right)$. Choose the correct option(s) related to diagram.

A cart of mass M is tied at one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. Initially, the man is at x = 0 and the cart at x = 10 m. If the man pulls the cart using the rope, the man and the cart will meet at the point

A galvanometer of resistance $20\Omega$ is to be converted into an ammeter of range $1A$. If a current of $1mA$ produces full-scale deflection, the shunt required for the purpose is

A beam of plane polarized light falls normally on a polarizer of cross sectional area $3\times {10}^{–4}{\text{m}}^2$. Flux of energy of incident ray is ${10}^{–3}$ Watt. The polarizer rotates with an angular frequency of $31.4{\text{rad s}}^{–1}$. The energy of light passing through the polarizer per revolution will be -

A ship $A$ is moving towards west with a speed of $10\text{km/h}$, and a ship $B$, $100\text{km}$ south of $A$, is moving towards north with the same speed of $10\text{km/h}$. The time after which the distance between them becomes shortest is

If S is stress and Y is Young’s modulus of material of a wire, the energy stored in the wire per unit volume is

A biker is performing stunt in a cylindrical death well of radius $16\text{m}$. If speed of biker is constant and coefficient of friction of well's surface is $0.2$, find the minimum speed required to perform the stunt safely.

Two particles $A$ and $B$ are moving with uniform velocity as shown in the figure given below at $t=0$.

Find out the shortest distance between the particles, if it occurs at $t=2.2\text{s}$

Find the centre of mass of a uniform $L$ shaped lamina (a thin flate plate) with dimensions as shown in figure. The mass of the lamina is $6\text{kg}$.

Angular momentum of body about a point $A$ is given as $\overrightarrow{L}=(4t^2+6)\hat{k}$. Find the net torque acting on body about point $A$ at $t=3\text{sec}$.

The diagram shows a scalene triangle, $ABC$, with vectors $\overrightarrow{AB}=\hat{a}$ and $\overrightarrow{AC}=2\hat{b}$. The point $D$ is positioned on the line $BC$ such that $BD:DC=3:2$. The point $E$ is positioned on the line $AD$ such that $AE:ED=1:2$. The expression for the vector $\overrightarrow{AE}$ in terms of $\hat{a}$ and $\hat{b}$ is

In the shown pulley-block system, strings are light. Pulleys are massless and smooth and system is released from rest. In $0.6$ second, what is the work done by gravity on $20\text{kg}$ and $10\text{kg}$ block respectively ?

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

A spherical body of radius $4\text{m}$ has a concentric cavity of radius $2\text{m}$ as shown in the figure. Thermal conductivity of the material is $\frac{100}{\pi }{\text{W/m}}^{\circ }\text{C}$. If the temperature of inner surface is kept at ${120}^{\circ }\text{C}$ and of the outer surface at ${40}^{\circ }\text{C}$. Then, find the temperature $T$ at a distance $3\text{m}$ from centre. (in ${}^{\circ }\text{C}$).

A particle travels $10\text{m}$ in first $5\text{sec}$ and $10\text{m}$ in next $3\text{sec}$. Assuming constant acceleration what is the distance travelled in next $2\text{sec}$

Two identical capacitors 1 and 2 are connected in series to a battery as shown in the figure. Capacitor 2 contains a dielectric slab of dielectric constant slab of dielectric constant K as shown. Q₁ and Q₂ are the charges stored in the capacitors. Now the dielectric slab is removed and the corresponding charges are then:

To test the quality of a tennis ball, you drop it onto the floor from a height of 4.00 m. It rebounds to a height of 2.00 m. If the ball is in contact with the floor for 12.0ms, then what is the average acceleration during that contact?

Find the moment of inertia (in ${\text{kg-m}}^2$) of a hollow cylinder of radius $3\text{m}$ and mass $3\text{kg}$, about an axis passing through the centre of the hollow cylinder. [Assume thickness of the hollow cylinder to be small]

If velocity of a particle is $v\left(t\right)=2t-4\text{m/s}$, the average speed and magnitude of average velocity of the particle in $5\text{sec}$ respectively are

An electron is taken from point A to point B along the path AB in a uniform electric field of intensity $E=10V{m}^{-1}$. Side AB = 5 m and side BC = 3 m. Then, the amount of work done on electron is

A nichrome element has a resistance of $75.3\Omega$ at ${27}^{\circ }C$. When 230 V p.d is applied and a study state temperature is reached, the current flowing through it is 2.68 A. If $\propto =1.7\times {10}^{-4\circ }{C}^{-1}$, find the steady state temperature

A projectile of mass $m$ is fired with a velocity $u$ from a point $P$ as shown. Neglecting air resistance, find the magnitude of the change in momentum of the projectile between the points $P$ and $Q$.

The tip of the seconds hand of a clock takes $60$ seconds to move once on the circular dial of the clock. If the radius of the dial of the clock be $10.5\text{cm}$ then calculate the speed of the tip of the seconds hand.

Initially, the spring is at its natural length and collision between blocks of mass $m\&m$ is elastic. The horizontal surface is smooth. Then, maximum compression of the spring during the motion will be:

The focus in terms of a parabolic mirror is where:

Two wires of same length are shaped into a square and a circle. If they carry same current, ratio of the magnetic moment is

An electric heater is used in a room of total wall area $137{\text{m}}^2$ to maintain a temperature of ${20}^{\circ }\text{C}$ inside it when the outside temperature is $-{10}^{\circ }\text{C}.$ The walls have three layers of different materials. The innermost layer is of wood of thickness $2.5\text{cm}$, the middle layer is of cement of thickness $1.0\text{cm}$ and the outermost layer is of brick of thickness $25\text{cm}$. Find the power of the electic heater. Assume that there is no heat loss through the floor and ceiling. The thermal conductivities of wood, cement and brick are $0.125{\text{W/m}}^{\circ }\text{C}$, $1.5{\text{W/m}}^{\circ }\text{C}$ and $1.0{\text{W/m}}^{\circ }\text{C}$ respectively.

According to Bohr's theory, the radius of the $n^{th}$ orbit of an atom of atomic number Z is proportional to

Ratio of longitudinal stress in case (I) & case (II) is

[Consider both wires are made of the same material]

A capacitor circuit is equipped with key switch $k$ as shown. Initially key switch is open. The excess charge flowing through the cell on closing the key $k$ is equal to

A stone falls freely under gravity. It covers distances $h_1,h_2$ and $h_3$ in the first $5$ seconds, the next $5$ second and the next $5$ seconds respectively. The relation between $h_1,h_2$ and $h_3$ is-

A rod is measured using a scale. The reading is $60\text{cm}$ at ${12}^{\circ }\text{C}$. If thermal coefficient of linear expansion of the rod is $3\times {10}^{-5}{/}^{\circ }\text{C}$, the reading of the rod at ${42}^{\circ }\text{C}$ is:

(Assume the scale does not expand)

A hollow spherical ball rolls on a table without slipping. Ratio of its rotational kinetic energy to its total kinetic energy is

A wire of uniform cross-section is bent in the shape shown in the figure. The coordinates of the centre of mass of each side are shown in the figure. Origin is taken at $O$. Find the coordinates of the center of mass of the given system.

A thief is running away on a straight road in a jeep moving with a speed of $9{\text{ms}}^{-1}$. A policeman chases him on a motor cycle moving at a speed of $10{\text{ms}}^{-1}$. If the instantaneous separation of the jeep from the motor cycle is $100\text{m}$, how long will it take for the policeman to catch the thief?

A projectile is thrown horizontally with a speed of $20{\text{m s}}^{-1}$. If $g$ is $10{\text{ms}}^{-2}$, then the speed of the projectile after $5$ seconds will be nearly

Two bodies of masses $2\text{kg}$ & $5\text{kg}$ have position vectors $\hat{i}-2\hat{j}+\hat{k}$ and $3\hat{i}+2\hat{j}-\hat{k}$ respectively. The centre of mass of the system has a position vector

If velocity v is given as v = a + bx + ct where a, b and c are constant and x and t are position and time, then which of the following is dimentionally correct?

A steel rod is streched along its length by $1\text{mm}$. The rod has initial length as $1\text{m}$ and cross sectional area $0.01{\text{m}}^2$. Young's modulus of steel is $2\times {10}^{11}\text{Pa}$. The potential energy stored in the steel rod assuming negligible change in volume due to streching of the rod is (in $\text{J}$):

The intensity of sound from a point source is $1.0\times {10}^{-6}{m}^{-2}$ at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source?

A transverse wave of amplitude $0.5\text{mm}$ and frequency $100\text{Hz}$ is produced on a wire stretched to a tension of $100\text{N}$. If the wave speed is $100\text{m/s}$. What average power is the source transmitting to the wire?

In the figure shown, if the block does not slide down the plane when a force of $\text{10 N}$ is applied perpendicular to the plane, find the coefficient of static friction between the plane and the block. Take $g=10m/s^2$

At t = 0, a transverse wave pulse in a wire is described by the function: $y=\frac{6}{x^2+3}$ where x and y are in meters. Write the function $y=(x,t)$ that describes this wave if it is traveling in the positive x-direction with speed of 5m/s.

Energy released when $1000$ small water drops each of same radius ${10}^{-7}\text{m}$ coalesce to form one large drop

(Surface tension of water is $7\times {10}^{-2}\text{N/m}$)

Two blocks ‘$A$’ and ‘$B$’ of same mass '$m$' connected by a light spring are suspended by a string as shown in figure. Find the acceleration of block ‘$A$’ and ‘$B$’ just after the string is cut.

Assertion & Reason type

Statement1: Electric field is always perpendicular to an equipotential surface.

Statement2: If there was a component of $\overrightarrow{E}$ along the surface, that would mean there is a potential change along that component and hence the surface is not equipotential.