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A body of mass 0.40 kg moving initially with a constant speed of $10m{s}^{-1}$ to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = -5 s, 25 s, 100 s.

A mass m is suspended from a rigid support P by means of a massless string as shown in the figure. A horizontal force F is applied at point O of the rope. The system is in equilibrium when the string makes an angle $\theta$ with the vertical. Then the relation between tension T, force F and angle $\theta$ is

What will be the speed of center of mass, if a solid sphere of radius 20 cm which rotates at 2 rps along a straight line?

A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is

Three resistors of 4 Ω, 12 Ω , and 6 Ω are connected in parallel No. of 12 Ω resistors required to be connected in parallel to reduce the total resistance to half of its original is

Suppose the glass of the previous problem is covered by a jar and the air inside the jar is completely pumped out.

(a) What will be the answers to the problem ?

(b) Show that the answers do not change if a glass of different shape is used provided the height, the bottom area and the volume are unchanged.

A wall has two layers $A$ and $B$, each made of different materials. Both the layers have the same thickness and cross secional area. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium, the temperature difference across the wall is ${36}^{\circ }C$. The temperature difference across the layer $A$ is

In a photodiode, the conductivity increases when the material is exposed to light. It is found that the conductivity changes only if the wavelength is less than 620 nm. What is the band gap ?

The temperature at which the root mean square velocity of a molecule will be doubled than at ${100}^{\circ }C$

Work done in charging a capacitor is stored in it in the form of electrostatic energy, given by

A 2 kg block is lying on a smooth table which is connected by a body of mass 1 kg by a string which passes through a pulley. The 1 kg mass is hanging vertically. The acceleration of block and tension in the string will be

Velocity $\left(V\right)$ versus displacement $\left(S\right)$ graph of a particle moving in a straight line is as shown in the figure. Given $V_0=4m/s$ and $S_o=20m.$ At $S=30m$, what is the acceleration of particle?

A heavy steel ball of mass greater than 1 kg moving with a speed of 2 $mse{c}^{-1}$collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed

Two satellites $S_1$ and $S_2$ revolve round a planet in coplanar circular orbits in the same sense. Their periods of revolution are 1 hour and 8 hours respectively. The radius of the orbit of $S_1$ is ${10}^4\text{km}$.

When $S_2$ is closest to $S_1$, find the speed of $S_2$ relative to $S_1$(in $kmph$)

A motor cyclist going round in a circular track at constant speed has

The ratio of Total energy and Potential energy of electron in Bohr orbit of $L{i}^{++}$ ion is:

How long will the ball take to come back to the point from where it was thrown?

A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is

Two cars A and B are traveling in the same direction with velocities $v_1$ and $v_2(v_1>v_2)$ When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

A slide projector has to project a 35 mm slide $(25\text{mm}\times 23\text{mm})$ on a $2\text{m}\times 2\text{m}$ screen at a distance of 10 m from the lens. What should be the focal length of the lens in the projector ?

A mass m = 8 kg is attached to a spring as shown in figure and held in position so that the spring remains unstretched. The spring constant is 200 N/m. The mass m is then released and begins to undergo small oscillations. The maximum velocity of the mass will be $(g=10m/s^2)$

An inductor -coil of inductance 17 mH is constructed from a cpper wire of length 100 m and cross sectional area 1 mm. caluclate the time constant of the circuit if this inductor is joined across an ideal battery The resistivity of copper $=1.7\times {10}^{-8}\Omega m.$

A certain triple-star system consists of two stars, each of mass $m$, revolving about a central star of mass $M$, in the same circular orbit. The two stars stay at opposite ends of a diameter of the circular orbit. Then the expression for the period of revolution $\left(T\right)$ of the stars is (radius of the orbit is $r$)

[NCERT 1982; CPMT 1989; DCE 2005]

A wire fixed at one end is stretched by constant force $F$. If elongation in wire is $l$, then energy stored in wire will be

A ball of mass 'm' moving horizontally at a speed 'v' collides with the bob of a simple pendulum at rest. The mass of the bob is also' 'm, if the collision is perfectly elastic, the bob of the pendulum will rise to a height of

A 100 W bulb has tungsten filament of total length 1.0 m and radius $4\times {10}^{-5}$ m. The emissivity of the filament is 0.8 and $\sigma =6.0\times {10}^{-8}W{m}^{-2}{K}^4$. Calculate the temperature of the filament when the bulb is operating at correct wattage.

Two particles A and B of masses $m_A$ and $m_B$ respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are $v_A$ and $v_B$ respectively, and the trajectories are as shown in the figure. Then

Motion of water in a vertical U - tube is SHM when water on one side is depressed a little and then released. Calculate the angular frequency of vibrations when height of water in U tube is 0.9 m.

A body starts from the origin and moves along the x-axis such that the velocity at any instant is given by (4t³- 2t), where t is in second and velocity in m/s. What is the acceleration of the particle, when it is 2m from the origin on positive side?

For the circuit shown in the figure, determine the charge of capacitor is steady state :

A string, fixed at both ends, vibrates in a resonant node with a separation of 2.0 cm between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. find the length of the string.

If for a given angle of projection, the horizontal range is doubled, the time of flight becomes

A polaroid is placed at 45^o to an incoming light of intensity I₀. Now the intensity of light passing through polaroid after polarisation would be

A disc of mass M and radius R is rolling with angular speed $\omega$ on a horizontal plane. The magnitude of angular momentum of the disc about the origin O is

Trajectory of particle in a projectile motion is given as $y=x-\frac{x^2}{80}$. Here, $x$ and $y$ are in metre. For this projectile motion match the following and select proper option $(g=10{\text{m/s}}^2)$:
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \text{Angle of projection}& \text{(p)}& 20\text{m}\\ \text{(B)}& \text{Angle of velocity}& \text{(q)}& 80\text{m}\\ & \text{with horizontal}& & \\ & \text{after}4s& & \\ \text{(C)}& \text{Maximum height}& \text{(r)}& {45}^{\circ }\\ \text{(D)}& \text{Horizontal range}& \text{(s)}& {\tan }^{-1}\left(\frac{1}{2}\right)\end{array}$

A simple pendulum fixed in a car has a time period of 4 seconds when the car is moving uniformly on a horizontal road. When the accelerator is pressed, the time period changes to 3.99 seconds. Making an approximate analysis, find the acceleration of the car.

One plate of a capacitor is connected to a spring as shown in figure. Area of both the plates is A. In steady state separation between the plates is 0.6 d (spring was to un stretched and the distance between the plates was d when the capacitor was uncharged. The force constant of the spring is

Calculate the mass of a ring with linear mass distribution $\lambda ={\lambda }_{0}si{n}^2\theta$ as shown in diagram. ${\lambda }_0$ = density at $\theta ={90}^{\circ }$.

A parallel-plate capacitor with plate area A and separation between the plates d is charged by a constant current i. Consider a plane surface of area $\frac{A}{2}$ parallel to the plates and drawn symmetrically between the plates. Find the displacement current through this area.

One mole of monoatomic gas is taken from point A to point B along path $A\to C\to B.$ Temperature at A is $T_0$, then heat absorbed in path ACB is

A block is kept on a horizontal table. The table is undergoing simple harmonic motion of frequency 3 Hz in a horizontal plane. The coefficient of static friction between the block and the table is 0.72. The maximum amplitude in cm of the table for which the block does not slip on the surface of the table is ___ . Take $g=10m{s}^{-2}$ .

A thin uniform rod of length l is pivoted at its upper end. It is free to swing in a vertical plane. Its time period for oscillations of small amplitude is