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A particle's position in the x-y plane varies as $x\left(t\right)=3t^3+4t^2,y\left(t\right)=16t^4+2$

Find the acceleration vector of the particle after 1 sec of start.

A dancer is rotating on a smooth horizontal floor with an angular momentum $L$. The dancer folds her hands so that her moment of inertia decreases by $25\%$. The new angular momentum is

Which of the following is the speed time graph of the given velocity time graph?

The moment of Inertia of a solid cylinder of mass '$M$' and radius $R$ about its Axis(as shown) is.

What is charge

The Van Der Waal’s equation of state for some gases can be expressed as: $(P+\frac{a}{V^2})(V-b)=RT$ Where $P$ is the pressure, $V$ is the molar volume and $T$ is the absolute temperature of the given sample of gas and $a,b$ and $R$ are constants.

Which of the following does not have the same dimension formula as that of $RT$ ?

A coil in shape of an equilateral triangle if side '|' is suspended between the pole pieces of a permanent magnet such that the magnetic field B is in the plane of the coil. If due to a current I in the triangle, a torque τ acts on it, the side of the triangle is:

If the sum of two unit vectors is a unit vector, then magnitude of difference is

Pressure is determined as force per unit area of the surface.The SI unit of pressure,pascal is as shown below:

1Pa=1N m^-2

If mass of air at sea level is 1034 g cm^-2 , calculate the pressure in pascal

A barometer kept in a stationary elevator reads 76 cm. If the elevator starts accelerating up the reading will be

Molar heat capacity of water in equilibrium with Ice at constant pressure is

Two conducting rings P and Q of radius r and 3r move in opposite directions with velocities 2v and v respectively on a conducting surface S.there is a uniform magnetic field of magnitude B perpendicular to the plane of the rings.The potential difference between the highest point of the two rings is:

A)zero

B)2Brv

C)6Brv

D)10Brv

From the top of a tower of height 10 m, one fire is shot horizontally with a speed of 5*root of 3/s. Another fire is shot upwards at an angle of 60 degrees with the horizontal at some interval of time with the same speed of 5*root of 3 m/s. The shots collide in air at a certain point. The time interval between the 2 shots?

A cart moves with a constant speed along a horizontal circular path. From the cart, a particle is thrown up vertically with respect to the cart, the particle will,

The acceleration- time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial velocity?

A particle of mass '$m$' is projected with velocity '$v$' an angle $\theta$ with the horizontal. Find its angular momentum about the point of projection when it is at the highest point of its trajectory?

A boy walks to his school at a distance of $6\text{km}$ with constant speed of $2.5{\text{km h}}^{-1}$ and walks back with a constant speed of $4{\text{km h}}^{-1}$. His average speed for round trip in ${\text{km h}}^{-1}$, is

A block of mass $m$ is stationary with respect to a rough wedge as shown in figure. Starting from rest in time $t$.
(Given that $m=1\text{kg},\theta ={30}^{\circ },a=2{\text{m/s}}^2,t=4\text{s}$)
Match Column $I$ with column $II$
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) Work done on block by gravity}& \text{(p)}144\text{J}\\ \text{(b) Work done on block by normal reaction}& \text{(q)}32\text{J}\\ \text{(c) Work done on block by friction}& \text{(r)}56\text{J}\\ \text{(d) Work done on block by all the forces}& \text{(s)}48\text{J}\\ & \text{(t)}\text{None}\end{array}$

A uniform thermometer scale is at steady state with its $0\text{cm}$ mark at ${20}^{\circ }\text{C}$ and $100\text{cm}$ mark at ${100}^{\circ }\text{C}$. Temperature of the $60\text{cm}$ mark is

A uniform chain of mass $m$ and length $L$ hangs on a table with two thirds of its length on the table. The work done by a person to put the hanging part back on the table will be

If the phase difference between the two wave is 2p during superposition, then the resultant amplitude is

[DPMT 2001]

A particle of mass 'm' moving eastward with a speed 'v' collides with another particle of the same mass 'm' and moving northward with the same speed 'v'. The two particles coalesce on collision. The new particle of mass '2'm will move in the north-easterly direction with a velocity

An uniform rod of mass $M$ & length $L$ is hinged about its one end as shown. Initially it is held vertical and then allowed to rotate, the angular velocity of rod when it makes an angle of ${37}^{\circ }$ with the vertical is

Blocks $A$ and $B$ of masses $2kg$ and $3kg$ respectively are placed on a smooth ground. If an external force $P$ of magnitude $10N$ acts on $A$ as shown, find the force exerted by $B$ on $A$ is

Given below are the equations of motion of four particles $A,B,C$ and $D$.
$x_A=6t-3$;
$x_B=4t^2-2t+3$;
$x_C=3t^3-2t^2+t-7$;
$x_D=7\cos 60°-3\sin 30°$
Which of these four particles move with uniform non-zero acceleration?

The coefficient of self inductance of a solenoid is $0.18$ mH. If a rod of soft iron of relative permeability 900 is inserted in it, then the coefficient of self inductance will become nearly

What will be the diameter (in $\text{mm}$) of a water droplet, the pressure inside which is $0.05{\text{N/cm}}^2$ greater than the outside pressure? (Take surface tension as $0.075\text{N/m}$).

The ratio of forces between two charges placed at a certain distance apart in air and at half the distance apart in medium of dielectric k is

A)1:4k

B)k:4

C)4k:1

D)4:k

Gravitational field at the centre of semicircle formed by a thin wire AB of mass m and length l is

To test the quality of a tennis ball, you drop it onto the floor from a height of 4.00 m. It rebounds to a height of 2.00 m. If the ball is in contact with the floor for 12.0ms, then what is the average acceleration during that contact?

A particle of small mass m is joined to a very heavy body by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

A cubical block of side ' a' is moving with velocity V on a horizontal smooth plane as shown in the figure. It hits a ridge at point O. The angular speed of the block after it hits O is

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.
The coordinates(meters) of the rabbit's position as function of time t(seconds) are given by

$x\left(t\right)=-\frac{t^2}{2}+5t+20Andy\left(t\right)=t^2-10t+30$

(a)At t=10s, what is the rabbot's position vector $\overrightarrow{r}$ in unit-vector notation and in magnitude-angle notation?

A particle is moving on x-axis has potential energy $U=2-20x+5x^2$ J along x-axis. The particle is released at x=-3. The maximum value of x will be [x is in meter and U is in joule]

Two masses $m_1=5\text{kg}\text{and}{m}_2=10\text{kg}$ connected by an inextensible string over a frictionless pulley are moving as shown in the figure. The coefficient of static friction of horizontal surface is 0.15. The minimum mass $m$ that should be put on top of $m_2$ to stop the motion is -

The time period of an artificial satellite in a circular orbit of radius R is 2 days and its orbital velocity is $v_0$. If time period of another satellite in a circular orbit is 16 days then

Three spheres, each of mass M and radius R, are arranged as shown in the figure. Then the moment of inertia of the system about $Y{Y}^1$

On an inclined plane of inclination ${30}^{\circ }$, a ball is thrown at an angle of ${60}^{\circ }$ with the horizontal, from the foot of the incline, with a velocity of $10\sqrt{3}{\text{ms}}^{-1}$. Then, the ball will hit the inclined plane in time: (take $g=10m{s}^{-2}$)

Which of the following are the necessary and sufficient conditions for a body to have some angular acceleration about a fixed Axis?

Particles of masses m, 2m, 3m ........... nm grams are placed on the same line at distances, l, 2l, 3l, ...... nl cm from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetres in

Two cylinders $A$ and $B$ having pistons contain equal amounts of an ideal diatomic gas at $300\text{K}$. The piston $A$ is free to move while the piston B is held fixed. Same quantity of heat is supplied to the gas in each cylinder. The temperature of the gas in cylinder $A$ rises by $35\text{K}$. The rise in temperature of the gas in cylinder $B$ is

Charges $Q_1$ and $Q_2$ are in vacuum initially. $Q_2$ experiences a net force F due to the presence of $Q_1$. They are now placed in a new medium of dielectric constant ε_rand the relative distance between them is maintained. The new net force experienced by $Q_2$ due to the presence of $Q_1$ is

AAball is released from the top of a tower of height h metres.I takes T seconds to reach the ground. What is the position of ball in the T/3 seconds?

prove the rotation v=w*r