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Find component of vector $\overrightarrow{A}$ along the direction of $\overrightarrow{B}$ i.e. A||B and in perpendicular direction of $\overrightarrow{B}$ that is $A_{{\perp }_B}$.

The speed of light $c$, gravitational constant $G$ and planck’s constant $h$ are taken as fundamental units in a system. The dimensions of time in this new system should be

Between the plates of parallel plate capacitor of capacitance C, two parallel plates, of the same material and area same as per the plate of the original capacitor, are placed. If the thickness of these plates is equal to ${\frac{1}{5}}^{th}$ of the distance between the plates of the original capacitor, then the capacitance of the new capacitor is

In the given figure, the velocity $v_3$ will be

A particle is executing a simple harmonic motion. Its maximum acceleration is $\alpha$ and maximum velocity is $\beta$. Then, its time period of vibration will be

Three blocks of mass $2\text{kg},3\text{kg}$ and $5\text{kg}$ are tied with three identical strings. The blocks are free to rotate in a vertical circle. The minimum velocity given to the blocks to complete the vertical circle is $v_1,v_2$ and $v_3$ respectively then

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have magnitude $3$ each. If $\overrightarrow{A}\times \overrightarrow{B}=-5\hat{k}+2\hat{i}$, then the angle between $A$ and $B$ is

A ball is thrown up from the top of a tower at 20 m/s velocity. It took the ball 6 sec to fall to the bottom. How high is the tower?

Light of wavelength $\lambda$ strikes a photo-sensitive surface and electrons are ejected with kinetic energy E. If the kinetic energy is to be increased to 2E, the wavelength must be changed to ${\lambda }^{\prime }$ where

The unit of momentum is

The potential energy (in joule) of a body of mass $2\text{kg}$ moving in the $x-y$ plane is given by $U=6x+8y$, where the position coordinates $x$ and $y$ are measured in meter. If the body is at rest at point $(6m,4m)$ at time $t=0$, it will cross the y – axis at time $t$ equal to

Two objects are thrown up at angles of ${45}^{\circ }$ and ${60}^{\circ }$ respectively, with the horizontal. If both objects attain same vertical height, then the ratio of magnitude of velocities with which they are projected is

Two masses $m_1=5kg$ and $m_2=10kg$ connected by an inextensible string over a frictionless pulley, as shown in the figure are moving . The coefficient of friction of horizontal surface is $0.15$. The minimum weight $m$ that should be put on top of $m_2$ to stop the motion is

Two equal forces$\left(F\right)$ have their resultant equal to either of the forces. Then, at what angle the forces are inclined?

A $800\text{kg}$ car takes a circular turn of radius $25\text{m}$ with an uniform speed of $36\text{km/h}$. The centripetal force acting upon the car is

A long spring is stretched by $2\text{cm}$. Its potential energy is $\text{U}$. If the spring is stretched by $10\text{cm}$, its potential energy would be

A geostationary satellite

The energy that should be added to an electron to reduce its de Broglie wavelength from one nm to 0.5 nm is

A rope of mass $5kg$ is moving vertically with an upward force of $100N$ acting at the upper end and a downward force of $70N$ acting at the lower end. The tension at the midpoint of the rope is

(Take $g=10m/s^2$)

The position of centre of mass of a system consisting of two particles of masses $m_1$ and $m_2$ separated by a distance L apart, from $m_1$ will be

Flux due to $q$ through square plate is

A body of mass $m=5\text{kg}$ is thrown at an angle $\theta ={30}^{\circ }$ to the horizontal with the initial velocity $v_0=20\text{m/s}$. Assuming the air drag to be negligible, find the magnitude of the momentum increment $\Delta p$ during the total time of motion.

Thermal coefficient of volume expansion at constant pressure for an ideal gas sample of $n$ moles having pressure $P_o$, volume $V_o$ and temperature $T_o$ is:

If velocity $v$, force $F$ and energy $E$ are taken as fundmental units, then dimensional formula for mass will be

Consider a special situtation in which both the faces of the block $M_0$ are smooth, as shown in adjoining figure. Mark out the correct statement(s)





(A) If $F=0$, the blocks $M$ and $m$ cannot remain stationary

(B) For one unique value of $F$, the blocks $M$ and $m$ remain stationary with respect to block $M_0$

(C) There exists a range of $F$ for which blocks $M$ and $m$ remain stationary with respect to block $M_0$

(D) Since there is no friction, therefore, blocks $M$ and $m$ cannot be in equillibrium with respect to block $M_0$

The elevator shown in fig. is descending with an acceleration of $2{\text{m/s}}^2$. The mass of the block $A=0.5\text{kg}$ and that of $B=1\text{kg}$. The force exerted by the block $A$ on block $B$ is

Find the maximum value of $F$ such that both the blocks move together. Take $g=10{\text{m/s}}^2$.

A body starts from rest. What will be the ratio of the distance travelled by the body during the $4^{th}$ and $3^{rd}$ second?

A prticle of mass $m$ moves with velocity $v_0=20\text{m/s}$ towards a large wall that is moving with velocity $v=5\text{m/s}$ towards the particle as shown. If the particle collides with the wall elastically, then find the speed of the particle just after collision. (Assume collision with the wall is elastic)

A current $I$ flows through a flat metal specimen of constant thickness and of the shape as shown in the figure. Given that $v_1,v_2$ and $v_3$ are mean drift speeds of the electron crossing the sections $P_1,P_2$ and $P_3$ respectively. Then

Two particles undergo SHM along parallel lines with the same time period $\left(T\right)$ and equal amplitudes. At a particular instant, one particle is at its extreme position while the other is at its mean position. They move in the same direction. They will cross each other after a further time of

Two particles having masses $m_1$ and $m_2$ are situated in a plane perpendicular to line AB at a distance of $r_1$and $r_2$ respectively as shown.

Find the moment of intertia about axis passing through centre of mass and perpendicular to line joining $m_1$ and $m_2$

A man running on a horizontal road at $8{\text{ms}}^{-1}$ finds rain falling vertically. If he increases his speed to $12{\text{ms}}^{-1}$, he finds that drops make ${30}^{\circ }$ angle with the vertical. Find the velocity of rain with respect to the road.

Arrangement of two block system is as shown. The net force acting on $1\text{kg}$ and $2\text{kg}$ blocks are (assuming the surfaces to be frictionless) respectively.

Internal resistance of a $2.1V$ cell which gives a current of 0.2 A through an external resistance of $10\Omega$ is

A car travels with the speed of $15\text{m/s}$ for $0<t\le 5\text{sec}$, $20\text{m/s}$ for $5<t\le 10\text{sec}$ and $5\text{m/s}$ for $10<t\le 15\text{sec}$. The total distance travelled by the car is

A pulley system is connected as shown in the figure. If the spring is elongated by a distance of $0.02\text{m}$, then what is the force constant of the spring? (Assume that the spring does not affect the overall acceleration of the bodies.)

A particle starting from rest undergoes acceleration given by $a=|t–2|{\text{m/s}}^2$ where, $t$ is time in second. Velocity of particle after $4\text{sec}$ is

In an L–R circuit $L=\frac{0.4H}{\pi }$ and R = 30 $\Omega$ If the circuit has an alternating emf of 220 volt and its frequency 50 cycles per sec, the impendence and current in the circuit respectively will be

Water from a tap emerges vertically downwards with an initial speed of $1\text{m/s}$. The cross-section area of the tap is ${10}^{-4}{\text{m}}^2$ . Assuming that the pressure is constant throughout the stream of water and the flow is steady, what will be the cross-section area of the stream $0.15\text{m}$ below the tap?

Three point masses $M_1=1.6\text{kg},M_2=2.4\text{kg}$ and $M_3=2\text{kg}$ are placed at the corners of a thin massless rectangular sheet $(1.2\text{m}\times 1.0\text{m})$ as shown in the figure below. Centre of mass of the system will be located at a point (assuming $M_1$ to be at the origin)

When the temperature of a rod increases from $t$ to $t+\Delta t$, the moment of inertia of the rod increases from $I$ to $I+\Delta I$. If the coefficient of linear expansion of the rod is $\alpha$, the ratio $\frac{\Delta I}{I}$ is

Find the value of $cos\left({24}^o\right)+cos\left(5^o\right)+cos\left({175}^o\right)+cos\left({204}^o\right)+cos\left({300}^o\right)$.

The pulley arrangements of figures (a) and (b) are identical. The mass of the rope is negligible. In Fig. (a), the mass m is lifted up by attaching a mass 2m to the other end of the rope. In Fig. (b) , m is lifted up by pulling the other end of the rope with a constant downward force F=2mg. The acceleration of m is the same in both cases.

A block of mass $m$ is kept on the floor of a freely falling lift. During the free fall of the lift, the block is pulled horizontally with a force of $F=5\text{N}.$ If coefficient of friction between block and floor is ${\mu }_s=0.1$, then the frictional force on the block will be

Dimensional formula for intensity of magnetising field and magnetic susceptibility are.