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A smooth block of mass m is placed on a smooth plank of mass M. The acceleration of M when it is acted by a force F is? Also find acceleration of m?

Find the amplitude of motion of the air in the path of a $40\text{dB},1000\text{Hz}$ sound wave.

[Assume that the density of air is $1.3{\text{kg/m}}^3$ and speed of sound in $340\text{m/s}$].

Wavelength of light used in an optical instrument are ${\lambda }_1=4000\dot{A}$ and ${\lambda }_2=5000\dot{A}$ then ratio of their respective resolving power is

A prism having an apex angle $4^{\circ }$ and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror

A boat is rowed perpendicular to river flow at the rate of $4.5\text{km/hr}$. The river flows at the rate of $6\text{km/hr}$. The speed of boat in $\text{m/s}$ is

A coil in the shape of an equilateral triangle of side $l$ is suspended between the pole pieces of a permanent magnet, such that magnetic field of intensity $B$ is along the plane of the coil. If due to a current $I$ in the triangle, a torque $\tau$ acts on it, then side $l$ of the triangle is :

The maximum height reached by projectile is $4\text{m}$. The horizontal range is $12\text{m}$. Velocity of projection in $\left({\text{ms}}^{-1}\right)$ is

($g$ is acceleration due to gravity)

In a photoelectric experiment for $4000\stackrel{\circ }{A}$

incident radiation, the potential difference to stop the ejection is 2 V. If the incident light is changed to $3000\stackrel{\circ }{A}$

, then the potential required to stop the ejection of electrons will be

If a liquid takes $30\text{s}$ in cooling from ${95}^{\circ }\text{C}$ to ${90}^{\circ }\text{C}$ and $70\text{s}$ in cooling from ${55}^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$ then temperature of room is -

If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $\lambda$. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be

In the shown figure, a particle of mass 'm' slides down the frictionless surface from height 'h' and collides with the uniform vertical rod of length L and mass M. After the collision, mass m sticks to the rod. The rod is free to rotate in a vertical plane about a fixed axis through O. Find the cosine of the maximum angular deflection of the rod from its initial position.

A solid sphere of mass $m$ is released from rest from the rim of a hemspherical cup so that it slides along the surface. If the rim of the hemisphere is kept horizontal, find the normal force exerted by the cup on the ball when the ball reaches the bottom of the cup. Neglect the radius of the ball as compared to the radius of the cup.

If $y=3x^2+2xthen\frac{dy}{dx}$=?

A uniform steel wire of length 4 m and area of cross-section $3\times {10}^{-6}{m}^2$ is extended by 1 mm by the application of a force. If Young's modulus of steel is $2\times {10}^{11}N{m}^{-2}$, the energy stored in the wire is

If a spring of spring constant $k$ extends by $x$ on loading due to an applied force $F$, then the energy stored by the spring is

A laser beam has intensity $I$. What is the amplitude of electric field in the beam?

Two containers of equal mass and containing equal volumes of water are placed on a balance as shown. The ball on the left is a ping pong ball and the ball on the right is made of steel. Both have equal volume. Towards which side will the balance tilt?

The particle moves in rectilinear motion as given in the acceleration – displacement $(a-s)$ curve shown in the figure. Determine the velocity after the particle has travelled $30\text{m}$, if the initial velocity is $10\text{m/s}$.

A cord is wound a round the circumfererence of a wheel of mass 50Kg and diameter 0.3m. The axis of the wheel is horizonatal. A mass of 0.5Kg is attached at the end of the cord. Find the angular acceleration of the wheel?

A rectangular plate of sides a and b is suspended from a ceiling by two parallel strings of length L each (figure). The separation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute simply harmonic motion. Find the time period.

Consider a small metallic plate of chromium, having only 5 free electrons on the surface. We shine light on the plate and we observe that these electrons come out but with different energies.

The energy received by each electron is 10 eV. Below is the list of energies with which each electron comes out.

e1 = 2.5 eV.

e2 = 2.7 eV.

e3 = 4.5 eV.

e4 = 5.5 eV.

e5 = 4.7 eV.

If one of these electrons has most optimally used the energy provided to come out, then what could be the work function of the metal chromium?

Twelve wires, each having equal resistance of 2 Ω, are joined to form a cube. The equivalent resistance between diagonally opposite points is .

A block of mass $m$ is moving down with constant velocity along an inclined plane of inclination $\theta$. What is the work done by an external force (applied parallel to the inclined plane) in pulling the block up the inclined plane through a height ${}^{\prime }{h}^{\prime }$ with constant velocity?

A shell initially at rest explodes into two pieces of equal mass, then the two pieces will

The ratio of average translational kinetic energy to rotational kinetic energy of a diatomic molecule at temperature T is

A ball of mass $50\text{g}$ is dropped from a height of $20\text{m}$. A boy on the ground hits this ball vertically upward with a bat with an average force of $200\text{N}$ so that it attains a vertical height of $45\text{m}$. The time for which the ball remains in contact with this bat is

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

A body cools from a temperature $3T$ to $2T$ in 10 minutes. The room temperature is $T$. Assume that Newton’s law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Which of the following expression is equal to $\cos \theta$, where $\theta$ is angle between $\overrightarrow{A}\text{and}\overrightarrow{B}$?

A wire abc is carrying current I. It is bent as shown in the figure and is placed in a uniform magnetic field B. Length ab = l and $\angle abc={45}^{\circ }$. What is the ratio of force on bc to that on ab?

What does an axiom mean?

Three processes form a thermodynamic cycle as shown on P - V diagram for an ideal gas.

Process $1\to 2$ takes place at constant temperature $300\text{K}$.

Process $2\to 3$ takes place at constant volume.

During this process $40\text{J}$ of heat leaves the system.

Process $3\to 1$ is adiabatic and temperature $T_3$ is $275\text{K}$.

Work done by the gas during the process $3\to 1$ is

Starting from the centre of the earth having radius $R$, the variation of $g$ (acceleration due to gravity) is shown by which of the following options

Two particle A and B move on a circle. Initially Particle A and B are diagonally opposite to each other. Particle A moves with angular velocity $\pi \frac{rad}{sec}$, angular acceleration $\frac{\pi }{2}\frac{rad}{se{c}^2}$ and particle B moves with constant angular velocity $2\pi \frac{rad}{sec}$. Find the time after which both the particle A and B will collide.

If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$, and $\overrightarrow{b}=\hat{j}-\hat{k}$ then area vector of plane formed by $\overrightarrow{a}$ and $\overrightarrow{b}$ is

The rms speed of oxygen at room temperature is about $500\text{m/s}$. The rms speed of hydrogen at the same temperature is about

Force of gravity is least at the_______.

The momentum in mechanics is expressed as $m$ x $v$. The analogous expression in electricity is

Which of the following is the speed time graph of the given velocity time graph?

Find the realation between the velocity of block $A$ and velocity of block $B$ in the shown figure.

The number of significant figures in $1.217\times {10}^{-4}$ is

A thin film of soap solution of refractive index $\mu$ and thickness t appears shining by a normal reflected light wavelength $\lambda$ then t can be

A man measures the time period of a simple pendulum inside a stationary lift and finds it to be $10\text{sec}$. If the lift accelerates upwards with an acceleration $\frac{g}{4}$, then find the time period of the pendulum.

The resistance of resistor at temperature $t^{o}C$ can be expressed as $R_t=R_0(1+2\gamma t+\varphi t^2)$, where $R_0$ is the resistance at $0^{o}C$ and $\gamma$,$\varphi$ are constants. The temperature coefficient of the resistance at $t^{o}C$ is

Average power in an A.C circuit is 50 watt. Resistance of circuit is $32\Omega$, and source voltage is 50V. Power factor of this circuit is

Ratio of volumetric stress & volumetric strain is given by

[Take $\left(\Delta P\right)$ to be change in pressure, $V$ as initial volume, $\Delta V$ as change in volume].

Light of frequency $4v_0$ is incident on the metal of the threshold frequency $v_0$. The maximum kinetic energy of the emitted photoelectrons is

Neon gas of a given mass expands isothermally to double of its original volume. What should be the further fractional decrease in pressure, so that the gas when adiabatically compressed from that state, reaches the original state?

A linear charge having linear charge density $\lambda$ penetrates a cube diagonally and then it penetrates a sphere diametrically as shown. What will be the ratio of flux coming out of cube and sphere?

Superman is going on a vacation to his home planet krypton from earth via. Sun. (Let's assume for a moment that Krypton is not destroyed). His energy v/s distance travelled graph is as shown below:



At which point is superman's (dE/ds) positive?