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A particle is placed at the origin. It starts from rest at $t=0$ and undergoes an acceleration $a$ as shown in the figure. Which of the following options correctly represent velocity $v$ vs. time $t$ and displacement $x$ vs. time $t$ plots?

The rise of the water level in a capillary tube of radius $0.07\text{cm}$ when dipped vertically in a beaker containing water (assuming it to be perfectly wetting) will be.

Given : Surface tension of water is $0.07{\text{Nm}}^{-1}$ and $g=10{\text{ms}}^{-2}$

When ${10}^{14}$ electrons are removed from a neutral metal sphere, the charge on the sphere becomes

Find $\overrightarrow{A}\times \overrightarrow{B}$, if $\overrightarrow{A}=3\hat{i}-\hat{j}+3\hat{k}$ and $\overrightarrow{B}=-2\hat{i}+3\hat{j}+4\hat{k}$

A block placed on a rough horizontal table is acted upon by an external horizontal force $P$. The graph of frictional force $F$ against external force $P$ is

Two bikes moving in opposite directions approach each other with speed of $40\text{m/s}$ and $20\text{m/s}$ respectively. The first bike sounds a horn having a frequency $380\text{Hz}$. The frequency heard by the biker of the second bike is

[velocity of sound in air is $340\text{m/s}]$

With what minimum acceleration can a fireman slide down a rope whose breaking strength is $\frac{2}{3}$ of his weight?

(Hint:-Use the concept of pseudo-force.)

Find the height of the center of mass of a semi-circular disk of radius $R=20\text{cm}$ from point $\text{O}$ (base center).

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

A projectile is fired at a speed of 100 m/s at an angle of ${37}^{\circ }$ above the horizontal. At the highest point, the projectile breaks into two parts of mass in ratio 1 : 3, the smaller coming to rest. Find the distance from the launching point to the point where the heavier piece lands.

If area of cross-section of both the limbs are equal, find the difference in heights of the liquid in the two limbs when the system is given an acceleration of $2{\text{m/s}}^2$ in horizontal direction as shown in figure. Neglect the width of the limbs.

At $t=0$, a particle starts from $(-1,0)$ and moves towards positive $x-$axis with speed of $v=3t^2+2t\text{m/s}$. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

You have been given a box filled with two gases - oxygen, and an unknown gas. It is seen that at any temperature of the mixture, the rms speed of the unknown gas is always four times that of oxygen. Can you identify this gas?

Four uniform rods of mass $m\text{kg}$ each form a rectangle as shown in figure. The rods have negligible area of cross-section. Find the position of center of mass of the rectangle made up of the four uniform rods.

An ideal choke takes a current of $10\text{A}$ when connected to an ac supply of $125\text{V}$ and $50\text{Hz}$. A pure resistor under the same conditions takes a current of $12.5\text{A}$. If the two are connected to an $\text{AC}$ supply of $100\text{V}$ and $40\text{Hz}$, then the current in a series combination of the above resistor and inductor is

In the above question, if the motion of the pulse and rotation of the loop, both are in same direction then the velocity of the pulse with respect to ground will be:

The focal lengths of the objective and eye-piece of a telescope are respectively $100cm$ and $2cm$. The moon subtends an angle of ${0.5}^{\circ }$ at the eye. If it is looked through the telescope, the angle subtended by the moon’s image will be

A metal wire having poisson ratio $1/4$ and young's modulus $4\times {10}^{10}{\text{N/m}}^2$ is stretched by a force, which produces a lateral strain of $0.01\%$ in it. The elastic potential energy stored per unit volume in wire is (in ${\text{J/m}}^3$)

A projectile is given an initial velocity of $\hat{i}+2\hat{j}$. The Cartesian equation of its path is

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

One end of a spring of length $\text{1}0\text{m}$ is attached to a block of mass $\text{5}\text{kg}$ which is rotated along a circular path with a linear velocity of $\text{1}\text{m/s}$. If the spring gets extended by a length of $\text{0}.025\text{m}$, find the spring constant.

A parallel-plate capacitor of area $A$, plate separation 𝑑, and capacitance $C$ is filled with four dielectric material having dielectric constants $k_1,k_2,k_3$ and $k_4$ as shown in the figure. If a single dielectric material is to be used to have the same capacitance $C$ in this capacitor, then its dielectric constant $k$ is given by

If a body looses half of its velocity on penetrating $3\text{cm}$ in a wooden block, then how much will it penetrate more before coming to rest?

The angle between the vector $2\hat{i}+4\hat{k}$ and the $Y$- axis is

A long uniform rod of length L and mass M is free to rotate in a vertical plane about a horizontal axis through its one end 'O'. A spring of force constant k is connected vertically between one end of the rod and ground. When the rod is in equilibrium it is parallel to the ground.

What is the period of small oscillations that result when the rod is rotated slightly and released?

Water is flowing through a horizontal tube of non-uniform cross section. At a place, the radius of the tube is $2\text{cm}$ and velocity is $6\text{m/s}$. What will be the velocity of water where the radius of pipe is $4\text{cm}$?

A screen is placed at a distance 40 cm away from an illuminated object. A converging lens is placed between the source and the screen and it is attempted to form the image of the source on the screen. If no position could be found, the focal length of the lens

When a dielectric slab is introduced between the plates of an isolated charged capacitor, it

A $10\text{g}$ bullet moving at $100\text{m/s}$ strikes a log. Assume that bullet undergoes uniform deacceleration and stops in $6.0\text{cm}$, find the magnitude of average force experienced by the log.

At some temperature T, a bronze pin is a little large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when

The ratio to radii of curvature of a biconvex lens $R_1:R_2$ = 2 : 3. Its refractive index and focal length is $1.5$ and $12cm$ respectively. What is the value of $R_1$? Consider $R_1$ and $R_2$ are positive and negative respectively.

The centre of mass of a uniform rod of length $10\text{m}$ is moving with translational velocity of $50\text{m/s}$ on a frictionless horizontal surface as shown in the figure and the rod rotates about its centre of mass with an angular velocity of $5\text{rad/sec}$. Find out the velocities of points $A$ and $B$.

A ball is thrown vertically downward with a velocity of $20\text{m/s}$ from the top of a tower. It hits the ground after some time with a velocity of $80\text{m/s}$. The height of the tower is :

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

In Young's double slit experiment, the two slits are illuminated by light of wavelength $5890\stackrel{\circ }{A}$ and the angular fringe width is ${0.2}^{\circ }$. If the whole apparatus is immersed in water, then the new angular fringe width will be (refractive index of water $=\frac{4}{3}$).

An object moves along the grid through the points A,B,C,D,E and F as shown in the figure. Find the distance covered by the moving object?

A particle is thrown with velocity u at an angle $\alpha$ from the horizontal. Another particle is thrown with the same velocity at an angle $\alpha$ from the vertical. The ratio of times of flight of two particles will be

A ray of light is incident on a plane mirror at an angle ${50}^{\circ }$. The deviation produced by the plane mirror will be

A $1\mu F$ capacitor holding a charge of $1\times {10}^{-5}C$ is connected to a $10\Omega$ resistor via switch.



What current will flow after the switch is closed?

A particle is projected with velocity $u$ at angle ${\theta }_1$ with horizontal. The ratio of range and maximum height is $4$.

When it is projected at angle ${\theta }_2$ with horizontal with same speed, the ratio of range and maximum height is $2$.

Then $\frac{\tan {\theta }_1}{\tan {\theta }_2}$ will be equal to

A ball of mass m falls vertically to the ground from a height $h_1$ and rebound to a height $h_2$. The change in momentum of the ball on striking the ground is

In a right angled triangle having hypotenuse 2 units.

If $\theta$ is included angle and $\sin \theta =\frac{1}{2}.$

Find the value of Adjacent side wrt included Angle $\theta$

If the surface shown in the figure is frictionless, and $T_1=6\sqrt{3}N$, find $F$.

In an insulator, the forbidden energy gap between the valence band and conduction band is of the order of

The moment of inertia of a rod of length 'l' about an axis passing through its centre of mass and perpendicular to rod is 'I'. The moment of inertia of hexagonal shape formed by six such rods, about an axis passing through its centre of mass and perpendicular to its plane will be

The logic circuit below has the input waveforms A and B as shown. Pick out the correct output waveform.

A circular disc is rotating with constant angular velocity ω about an axis that passes through the centre. A particle 'P' is kept at a distance of 2m from the centre and another particle 'Q' at a distance of 3m from the centre.

Which of these will have higher centripetal acceleration?

A small ring is attached to the vertical ring as shown in the figure. The small ring is given velocity $v_B=\sqrt{4gl}$ by a sharp hit, where $l$ is the radius of the vertical ring. Find the normal force acting on the small ring at the topmost point, if the mass of the small ring is $m$.