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The contact force between $2\text{kg}$ and $3\text{kg}$ block placed on an inclined plane as shown in the figure will be

A body of mass M is kept on a rough horizontal surface (friction coefficient = $\mu$). A person is trying to pull the body by applying a horizontal force but the body is not moving. The force by the surface on the body is F, where

The angle of incidence for an equilateral prism is ${60}^{\circ }$. What should be the refractive index of prism so that the ray is parallel to the base inside the prism?

If the speed of a particle is given as $v=6t^2+2t\text{m/s}$, the speed of the particle at $2\text{sec}$ and the average speed in $4\text{sec}$ respectively is

Two bodies $A$ (of mass 1 kg) and $B$ (of mass 3 kg) are dropped from height of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is

If $u_1$ and $u_2$ are the units selected in two systems of measurement and $n_1$ and $n_2$ are their numerical values respectively, then for constant physical quantity

An ant moves from A to B and then comes back to point A. Find the distance (d) and displacement (s) of the ant in this entire journey.

If the intermolecular forces vanish away, the volume occupied by the molecules contained in $4.5\text{kg}$ water at STP will be

An air bubble in sphere having 4 cm diameter appears 1 cm from surface nearest to eye when looked along diameter. If _am_g = 1.5, the distance of bubble from refracting surface is

[CPMT 2002]

A car moves along a straight line whose equation of motion is given by $s=24t+3t^4–2t^3$, where $s$ is in metre and $t$ is in second. The velocity of the car at $t=0$ will be

A moderator in a nuclear reactor serves to

A flywheel rotates at a costant speed of $3000$ rpm. How much time will it take to describe the angle of 100$\pi$ rad?

A tank used for filling helium balloons has a volume of $0.3{\text{m}}^3$ and contains $2\text{mol}$ of helium gas at ${20}^{\circ }\text{C}$. Assuming that the helium behaves like an ideal gas, find the total translational kinetic energy of the molecules of the gas

Velocity of a particle is in negative direction with constant acceleration in positive direction. Then, match the following columns.

An AIR station is broadcasting the waves of wavelength 300 metres. If the radiating power of the transmitter is 10 kW, then the number of photons radiated per second is

A particle is thrown up inside a stationary lift of sufficient height and the time of flight is $T$. Now it is thrown again with same initial speed $V_0$ with respect to the lift. At the time of second throw, lift is moving up with speed $V_0$ and uniform acceleration $g$ (where $g$ is the the acceleration due to gravity). The new time of flight will be.

Three blocks, each of same mass m, are connected with wires $W_1$ and $W_2$ of same cross- sectional area a and Young's modulus Y. Neglecting friction the strain developed in wire $W_2$ is

In a photo cell, the photo-electrons emission takes place

A particle executes linear simple harmonic motion with an amplitude of $3cm$. When the particle is at $2cm$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is

A ray of light is incident at angle $i$ on a surface of a prism of small angle $A$ and emerges normally from the opposite surface. If the refractive index of the material of the prism is $\mu$, the angle of incidence $i$ is nearly equal to:

A particle $P$ is sliding down a frictionless hemispherical bowl. It passes the point $A$ at $t=0$. At this instant of time, the horizontal component of its velocity is $v$. A bead $Q$ of the same mass as $P$ is ejected from $A$ at $t=0$ along the horizontal string $AB$, with the speed $v$. Friction between the bead and the string may be neglected. Let $t_P$ and $t_Q$ be the respective times taken by $P$ and $Q$ to reach the point $B$. Then:

Dimensional formula of heat energy is

Velocity of a particle travelling along a straight line represented by $+ve$ $x$-axis is given by

$4$ $0\le t<5$

$v\text{(m/s)}$ $=$ $2t$ $5\le t<10$

$6t^2$ $10\le t\le 20$

Find out the distance travelled by the particle between $t=4\text{s}$ to $t=12\text{s}$.

The liquids shown in figure in the two arms are mercury (specific gravity = 13.6) and water. if the difference of heights of the mercury columns is 2 cm, find the height h of the water column.

A body of mass 40 kg having velocity 4 m/s collides with another body of mass 60 kg having velocity 2 m/s. If the collision is inelastic, then loss in kinetic energy will be

Two glass bulbs of equal volumes connected by a narrow tube are filled with a gas at $0^{\circ }C$ and a pressure of 76 cms of Hg. One of the bulbs is then placed in a water bath maintained at ${62}^{\circ }C$. What is the new value of the pressure inside the bulb? The volume of connecting tube is negligible

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures $t_1$ and $t_2$ of the liquid, fractions $f_1$ and $f_2$ of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

The compressibility of a material is

A thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects, each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity

The energy stored in a condenser of capacity C which has been raised to a potential V is given by

A charged particle of mass 1.0 g is suspended through a silk thread of length 40 cm in a horizontal electric field of intensity $4.0\times {10}^{4}N{C}^{-1}$ as shown in the figure. If the particle stays in equilibrium at a distance of 24 cm from the wall, find the net charge on the particle?

A point moves rectilinearly with deceleration which depends on the velocity $v$ of the particle as $a=k\sqrt{v}$, where $k$ is a positive constant. At the initial moment the velocity of the point is equal to $v_0$. What distance will it cover before it stops ?

Which of the points marked in the figure below are in phase?

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. After collision, they fly apart in opposite directions with equal speeds. The ratio of masses $\frac{m_A}{m_B}$ is

A wheel starting with angular velocity of $10\text{rad/sec}$ acquires angular velocity of $100\text{rad/sec}$ in $15\text{seconds}$. If angular acceleration of wheel is constant, what will be the angular displacement of a point on the wheel in $15\text{seconds}$?

A stone thrown upward with a speed $u$ from the top of a tower reaches the ground with a speed $4u$. The height of the tower is

A block with a mass of $1\text{kg}$ is connected to a massless spring with a force constant of $100\text{N/m}$ and is placed on a smooth horizontal surface. At $t=0$, a constant force of $F=10\text{N}$ is applied on the block, when the spring is in its natural length. The speed of the block, when it is displaced by $8\text{cm}$ from its mean position will be

A simple harmonic wave is represented by the relation

$y(x,t)=A\sin 2\pi (vt-\frac{x}{\lambda })$

If the maximum particle velocity is three times the wave velocity, the wavelength $\lambda$ of the wave is

Find the torque by the force, $\overrightarrow{F}=2\hat{i}+3\hat{j}+5\hat{k}$ acting at the point $\overrightarrow{r_1}=5\hat{i}+2\hat{j}-\hat{k}$ about the point $\overrightarrow{r_2}=6\hat{i}-4\hat{j}+\hat{k}$.

From the figure, a thin wire is stretched by a block going over a pulley. The wire vibrates in its fifth harmonic in resonance with a particular tuning fork. When a beaker containing a liquid of density $800{\text{kg/m}}^3$ is brought under the block so that the block is completely dipped into the liquid, the wire vibrates in its sixth harmonic in resonance with the same tuning fork. If the density of material of the block is $2.6\times {10}^x{\text{kg/m}}^3$, then what is the value of $x$?

In a given circuit, if peak voltage across resistance is 8V, then the value of capacitance is

The coefficient of static and kinetic friction between a body of mass $m=1$ unit and the surface are $.75$ and $.50$ respectively. A force is applied to the body to maintain constant acceleration when the body is in motion. This constant force is:

The bob of a simple pendulum has a mass m and it is executing simple harmonic motion of amplitude A and period T. it collides with a body of mass $m_0$ placed at the equilibrium position which sticks to the bob. The time period of the oscillation of the combined masses will be

An infinitely long conductor PQR is bent to form a right angle as shown. A current I flows through PQR The magnetic field due to this current at the point M is $H_1$. Now another infinitely long straight conductor QS is connected at Q so that the current is I/2 in QR as well as in QS, The current in PQ remaining unchanged. The magnetic field at M is now $H_2$ The ratio $\frac{H_1}{H_2}$ is given by

When source and detector are stationary but the wind is blowing at speed , the apparent wavelength ${\lambda }^{\prime }$ on the wind side is related to actual wavelength $\lambda$ by [take speed of sound in air as v]

The length of an elastic rod is $a$ when tension is 4 N and $b$ when the tension is 5N. The length of the rod when tension is 9N is

Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is