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A body, initially at rest, is acted upon by four forces $\overrightarrow{F_1}=\hat{i}+\hat{k},\overrightarrow{F_2}=2\hat{j}+3\hat{k},\overrightarrow{F_3}=3\hat{i}$ and $\overrightarrow{F_4}=3\hat{j}-4\hat{i}$. In which plane will the body move?

A long solid cylindrical conductor of radius $10\text{cm}$ carries a current of $4\text{A}$ which is uniformly distributed over its circular cross-section. The magnetic field at a distance of $5\text{cm}$ from the axis of the conductor is

A and B are two wave trains shown in the figure, the ratio of intensity of A to B is

A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. The work one in stretching the wire by an amount x is given by

A capacitor of capacitance $2.0\mu F$ is charged to a potential difference of 12 V. It is then connected to an uncharged capacitor of capacitance $4.0\mu F$ as shown in figure (31-E22). Find (a) the charge on each of the two capacitors after the connection, (b) the electrostatic energy stored in each of the two capacitors and (c) the heat produced during the charge transfer from one capacitor to the other.

Two cars are moving in the same direction with a speed of $30{\text{km h}}^{-1}$. They are separated from each other by $5\text{km}$. Third car moving in the opposite direction meets the two cars after an interval of 4 minutes. What is the speed of the third car?

The variation of velocity of a particle moving along a straight line is shown in the figure. The magnitude of displacement of the particle in $8\text{s}$ is:

A spacecraft of mass M explodes into two parts when its velocity is V. After the explosion, one part of mass m is left stationary. What is the velocity of the other part?

A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by the particle on the wall and the acceleration of the particle varies with x (distance of the particle from the centre) according to

A ball is projected with an initial speed $u$ at an angle $\theta$ from the horizontal ground. The coefficient of restitution between the ball and the ground is $e$. Find the position from the starting point when the ball will land on the ground for the $2^{nd}$ time.

A truck of mass $2000kg$ travelling at $4\text{m/s}$ comes to rest in $2\text{s}$ when it strikes a wall. Force exerted by the wall is

A parallel plate condenser is filled with two dielectrics as shown.


Area of each plate is $A$ $m^2$ and the separation is $t$ m. The dielectric constants are $k_1$ and $k_2$ respectively. Its capacitance in farad will be

Two monochromatic sinusoidal waves, each of intensity $I$, have a constant phase difference of $\varphi$. These waves when superimposed, form a resultant sinusoidal wave. Then, the intensity of the resultant wave is

If $\overrightarrow{a}=\hat{i}+\hat{j},\overrightarrow{b}=\hat{i}+\hat{k},$ then $\{\{(\overrightarrow{a}\times \overrightarrow{b})\times \overrightarrow{a}\}\times \overrightarrow{a}\}\times \overrightarrow{b}=$

A spring block arrangement is shown in the figure.


The spring is stretched along the inclined plane from position $A$ (unstretched) to position $B$. Find the change in potential energy of the spring.

A dipole of dipole moment 20 ×10^-6 is present inside a surface.what is net outward flux

The upper end of a wire (diameter $12\text{mm}$ and length $1\text{m}$) is clamped and its other end is twisted through an angle of ${30}^{\circ }$. The angle of shear is

In
an accelerator experiment on high-energy collisions of electrons with
positrons, a certain event is interpreted as annihilation of an
electron-positron pair of total energy 10.2 BeV into two γ-rays
of equal energy. What is the wavelength associated with each γ-ray?
(1BeV = 10⁹
eV)

A thin uniform rod AB of mass M and length L is hinged at one end A to the horizontal floor. Initially it stands vertically. It is allowed to fall freely in a vertical plane. If the linear speed of B when it hits the floor is $\sqrt{\frac{xg}{L}}$, what is x?___

A wire of length $1\text{m}$ and area of cross-section $4\times {10}^{-8}{\text{m}}^2$ increase in length by $0.2\text{cm}$ when a force of $16\text{N}$ is applied. The value of $Y$ for the material of the wire will be

If motion of a particle is represented by $s=e^t+4^t-\cos t$, then the acceleration of the particle at any time $t$ is
[Hint: Acceleration of the particle is $\frac{d^{2}s}{d{t}^2}$]

A certain charge $Q$ is divided into two parts, $q$ and $Q-q$. How should the charges be divided so that $q$ and $Q-q$ placed at a certain distance apart, experience maximum electrostatic repulsion?

Two point charges 100μc and 5μc are placed at points A and B respectively with AB=40 cm . The work done by external force in displacing the charge 5μc from B to C , where BC=30 cm, angle $ABC=\frac{\pi }{2}and\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N{M}^2/c^2$

A balloon is moving vertically with a velocity of $4\text{m/s}$. When it is at a height of $h$, a ball is gently released from it. If it reaches the ground in $4\text{s}$, the height of the balloon when the body is released is

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A projectile is thrown with a speed of 10√2 m/s at an angle of 45⁰ with the horizontal. The Time interval between the moments when its speed is √125m/s is (g = 10m/s²)

Find the maximum velocity for skidding for a car moved on a circular track of radius 100 m. The coefficient of friction between the road and tyre is 0.2

In the circuit shown in the figure, the ac source gives a voltage $V=20\cos \left(2000t\right)$. Neglecting source resistance, the voltmeter and ammeter readings will be

A vertical glass capillary tube open at both ends contains some water. Which of following shapes may be taken by the water?