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A trolley carries a body of weight $25kg$. which is kept at a distance of $2.5m$ from the rear end of the trolley. The trolley starts from rest and accelerates at a constant rate of $2m{s}^{-2}$ If the coefficient of friction between the trolley and the body is $0.1$, find the distance of the trolley from the starting point where the body will just slip out of the trolley. $\text{Take}g=10m{s}^{-2}$

The storage battery of
a car has an emf of 12 V. If the internal resistance of the battery
is 0.4Ω, what is the maximum
current that can be drawn from the battery?

A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $20m{s}^{-1}$. A second player on the goal line $60m$ away in the direction of kick starts running to receive the ball at that instant. Find the speed $\left(m/s\right)$ of the second player with which he should run to strike the ball before it strikes the ground $(g=10m{s}^{-2})$

1. 0.19

The length of needle floating on the surface of water is $2\text{cm}$. Find the force in addition to its weight required to lift needle from the water surface. (Surface tension of water $=7.5\text{N/cm}$)

A single slit diffraction pattern is formed with white light. For what wavelength of light, the third secondary maximum in the diffraction pattern coincides with the second secondary maximum of red light in the pattern. Take wavelength of red light as $6500\mathring{\text{A}}$?

A wheel completes 2000 revolutions to cover the 9.5 km. distance. then the diameter of the wheel is

A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=kt$ ($k$ is a constant) acts along along the direction of motion of particle for the time interval $T$ so that its momentum changes from $p$ to $5p$. The value of $T$ is

1. 25

A particle is projected upwards with velocity $v=30\text{m/s}$. There are two points $A$ and $B$ at heights $h_A=25\text{m}$ and $h_B=40\text{m}$. If the particle crosses point $B$ twice in a time interval $\Delta t$ then it will also cross $A$ twice in a time interval equal to $(g=10{\text{m/s}}^2)$

In the kinetic theory of gases, we try to relate macroscopic properties of a gas, like pressure, volume and temperature to its microscopic properties (properties of each atom or molecule) like particle speeds, momenta, kinetic energies, etc. Which of the following is/are incorrect assumption(s) for building the theory?

Which of the following diagram correctly represents the working of a Carnot's refrigerator?

A particle is moving in a circle of radius $R$ with constant speed. The time period of the particle is $T$. In a time $t=\frac{T}{6}$
16. Average speed of the particle is

A string fixed at both ends has consecutive standing wave modes for which the distance between adjacent nodes are $12\text{cm}$ and $10\text{cm}$ respectively. If the tension is $20\text{N}$ and the linear mass density is $8\text{g/m}$, what is the fundamental frequency?

An object of length 2.0 cm is placed perpendicular to the principal axis of a convex lens of focal length 12 cm. Find the size of the image if the object is at a distance of 8.0 cm from the lens.

A trolley filled with sand is moving with a velocity of $v$ on a smooth horizontal surface. If the sand starts falling off at the rate of $\mu \text{kg/s}$ from the hole at its bottom, the velocity$\left(v\right)$ of the trolley as a function of time$\left(t\right)$ will be best represented by -

A potential barrier of $0.5\text{V}$ exists across a P-N junction. An electron approaches the junction from inside, with a speed of $5\times {10}^5\text{m/s}$. With what speed will it enter the P-side?

One mole of an ideal gas is heated slowly so that it goes from the $P-V$ state $(P_i,V_i)$ to $(3P_i,3V_i)$ in such a way that the pressure of the gas is directly proportional to the volume. How much work is done on the gas in the process?

Young's double slit experiment is carried out using microwaves of wavelength $\lambda =3\text{mm}.$ Distance between the slits is $d=5\text{mm}$ and the distance between the plane of slits and the screen is $D=100\text{cm}$. Find the total number of maxima formed on the screen.

Which of these objects' length/height is measured in m?

A body is sliding down a rough inclined plane of angle of inclination $\theta$ for which coefficient of friction varies with distance $y$ as $\mu \left(y\right)=Ky$, where $K$ is constant. Here $y$ is the distance moved by the body down the plane. The net force on the body is zero at $y=A$. Find the value of constant $K$.

Find the projection of $\overrightarrow{A}=\hat{i}+\hat{j}+\hat{k}$ along the vector $\overrightarrow{B}=2\hat{i}-\hat{j}+\hat{k}$

A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$, with its polarization along the direction $\hat{k}$. The correct form of the magnetic field of the wave would be (here $B_0$ is an appropriate constant):

A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a voltage $V$. Another capacitor of capacitance $2C$ is similarly charged to a voltage $2V$. The batteries are disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other capacitor. The final energy of the configuration is

A cannon of mass $m_1$ fires a shell of mass $m_2$ with speed $v_0$ relative to the barrel which is inclined at an angle $\alpha$ with horizontal . Find the recoil speed of cannon if it is placed on ice.