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A satellite is to revolve round the earth in a circle of radius 8000 km. With what speed should this satellite be projected into orbit? What will be the time period ? Take g at the surface = 9.8 m/$s^2$ and radius of the earth = 6400km.

If a body has a charge of magnitude $8\times {10}^{–19}$ coulomb what is the correct combination of protons and electrons on it?

If the length of a cylinder is measured to be $4.28\text{cm}$ with an error of $0.01\text{cm}$, then the percentage error in the measurement will be

A particle moves in the $x-y$ plane under the influence of a force such that its linear momentum is $\overrightarrow{p}\left(t\right)=A\left[\cos \right(kt)\hat{i}-\sin (kt\left)\hat{j}\right]$, where $A$ and $k$ are constants. The angle between the force and the momentum is :

Two plates 1 and 2 move with velocities $v$ and $2v$ as shown. If the sphere does not slide relative to the plates and assuming the mass of each body as $m$, find the kinetic energy of the system (plates + sphere).

Velocity-time equation of a particle moving in a straight line is, $v=(2t+3t^2)$. Find displacement of particle from the origin at time $t=1\text{s}$, if it is given that displacement is $10\text{m}$ at time $t=0$

A one kilowatt motor pumps out water from a $\text{10 m}$ deep well. Calculate the quantity of water pumped out per second.(Take $g=10\text{m}/{\text{s}}^2$)

A wheel is making rotations about its axis with uniform angular acceleration. Starting from rest, it reaches 100 rot/s in 4 seconds. It's angular acceleration is

What is the error in the area of a rectangle?

Given: L=5 $\pm$ 1 units

B= 4$\pm$2 units

Three identical carrom coins, each of radius $5\text{cm}$ are placed touching each other on a horizontal surface such that an equilateral triangle is formed when the centres of the coins are joined. Find the coordinates of this centre of mass, if the origin is fixed at the centre of coin A, as shown in figure.

The position vector of three particles of mass $m_1=3\text{kg},m_2=4\text{kg}$ and $m_3=1\text{kg}$ are $\overrightarrow{r_1}=(2\hat{i}+\hat{j}+3\hat{k})\text{m},\overrightarrow{r_2}=(\hat{i}-3\hat{j}+2\hat{k})\text{m}$ and $\overrightarrow{r_3}=(3\hat{i}-2\hat{j}-\hat{k})\text{m}$ respectively. Find the position vector of centre of mass of the system of particles.

In the system as shown, mass of the block is 1kg and spring constant is 25 $\frac{N}{m}$. The maximum kinetic energy of the block is 50J.

If $(\overrightarrow{A}+\overrightarrow{B})$ is perpendicular to $\overrightarrow{B}$ and $\overrightarrow{A}+2\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$, then

Write the equation of the wave shown in figure, if its position is shown at $t=0.6\text{sec}$. The wavelength is $15\text{cm}$ and amplitude is $4\text{cm}$ and the crest $X$ was at $x=0$ at $t=0$.

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:

Find the number of positions where $\frac{dE}{ds}$=0. Based on this find out the number of stars that Super man crossed on his way home from earth. (I hope you know that superman's source of energy is sunlight or star light so the more closer he goes to a star the more energy he has)

For the body shown in the figure:





Statement $1:I_z=I_x+I_y$

Statement $2:I_x=I_z+I_y$ and $I_y=I_x+I_z$

where $x$, $y$ and $z$ are the axes of rotation of the body.

Choose the correct option.

It is raining vertically with a velocity of $25{\text{ms}}^{-1}$. A woman rides a bicycle with a speed of $10{\text{ms}}^{-1}$ in north to south direction. What is the direction (angle with vertical) in which she should hold her umbrella to save herself from the rain?

Pick the correct option - If all matter were made of electrically neutral particles such as neutrons,

Quantam nature of light is explained by which of the following phenomenon

A block of mass $4\text{kg}$ is kept on ground. The co-efficient of friction between the block and the ground is $0.8$. An external force of magnitude $30\text{N}$ is applied parallel to the ground. The resultant force exerted by the ground on the block is

(Take $g=10{\text{m/s}}^2$)

A particle is at rest at a point $(4,3,0)$. Due to an impulse, it gets linear momentum $\overrightarrow{P}=\hat{i}+2\hat{j}$. The angular momentum of the particle about the origin is

Force $\overrightarrow{F_1}=(2\hat{i}–3\hat{j})\text{N}$ and $\overrightarrow{F_2}=(-5\hat{i}+2\hat{j})\text{N}$ act through the points whose position vectors are $\hat{k}$ and $3\hat{k}$ respectively. The vector sum of the torque due to these forces is

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left(x\right)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D=[U_{x=\infty }-U_{\text{at equilibrium}}]$, $D$ is

A force applied by an engine of a train of mass $2.05\times {10}^6\text{kg}$ changes its velocity from $5\text{m/s}$ to $25\text{m/s}$ in $5\text{minutes}$. The power of the engine is

If I have two vectors of length 3 and 4. What are the maximum and minimum possible lengths of the resultant?

A ball is thrown vertically upwards with velocity of $10\text{m/s}$ from the top of a tower. It returns to ground after some time with speed of $60\text{m/s}$. The height of the tower is



$(g=10{\text{m/s}}^2)$

The Young’s modulus of brass and steel are $10\times {10}^{10}N{m}^{-2}and2\times {10}^{11}N{m}^{-2}$ respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are $R_B$ and $R_s$ respectively. Then

Axis of a solid cylinder of infinite length and radius $R$ lies along $y$-axis. It carries a uniformly distributed current $‘i^{\prime }$ along $+y$ direction. Magnetic field at a point $(\frac{R}{2},y,\frac{R}{2})$ is

A steam cylindrical pipe of inner radius $5\text{cm}$ and outer radius $7\text{cm}$, having conductivity $0.07\text{W/mK}$, carries steam at ${100}^{\circ }\text{C}$. If the temperature at the outer wall of the pipe jacket is ${20}^{\circ }\text{C}$, then find the heat lost through the jacket per metre length in an hour.

A particle executes linear simple harmonic motion with an amplitude of $3\text{cm}$. When the particle is at $2\text{cm}$ from the mean position, the magnitude of its velocity is equal to that of its acceleration. Find the time period in seconds.

A uniform thin rod of mass $m$ and length $R$ is placed normally on surface of earth as shown. The mass of earth is $M$ and its radius is $R$. Then the magnitude of gravitational force exerted by earth on the rod is :

An object is projected at an angle of ${45}^{\circ }$ with the horizontal. The horizontal range and the maximum height reached will be in the ratio.

The coordinates of a moving particle at any time ${}^{\prime }{t}^{\prime }$ are given by $x=t^3$ and $y=4t^2$, where $x$ and $y$ are in metre and $t$ in second. The acceleration of the particle at time $t=1s$ is given by

What is the average velocity during time interval $t=2\text{s}$ to $t=5\text{s}$, in the following position time curve?

A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$, which can slide freely along the rod. Initially, the two beads are at the centre of the rod and the system is rotating with angular velocity ${\omega }_0$ about an axis perpendicular to the rod and passing through the mid-point $C$ of the rod. There are no external forces. When the beads reach the ends of the rod, then angular velocity of the system is

An infinite ladder is constructed with 1 $\Omega$ and 2 $\Omega$ resistors as shown in figure. Find the total current provided by the battery of EMF 12 V?

An object A is released from the top of a vertical building of height $H$. At an instant when it has descended $xm$ from the top, another object B is released from $ym$ below the top of that building. Right from this instant, both these objects take the same amount of time to reach the ground. Which of the following expressions in the given situation is correct ?

Five uniform circular plates, each of diameter $b$ and mass $m$, are placed together to form a pattern as shown in the figure. Find the $y$ coordinate of the centre of mass of the system.

A particle moves in a circle of radius $3.5\text{cm}$ at a speed given by $v=8t$, where $v$ is in $\text{cm/s}$ and $t$ in seconds. Find the tangential acceleration at $t=2\text{s}$. (in ${\text{cm/s}}^2)$

A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

What is the unit of conductivity and resistivity respectively?

The typical ionisation energy of a donor in silicon is

In the figure shown, find the velocity acquired by the block on reaching the ground and the force exerted by the inclined plane on the block if takes 5 seconds for the block to reach the ground. Assume all surfaces to be smooth. (Take $g=10m/s^2)$