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A block of mass $4\text{kg}$ is placed on a rough horizontal plane. A time depedent force $F=k{t}^2$ acts on the block, where $k=2{\text{N/s}}^2$. Coefficient of static friction $\mu =0.8$. Force of friction between the block and the plane at $t=2\text{s}$ is

A cubical wooden box of side $L$ is placed on a horizontal rough surface and the coefficient of static friction between them is $\mu$. Another cubical box of the same wood but of side $2L$ is placed on the same surface. Then the coefficient of static friction is

What is the acceleration of the ball at the highest point?

In the figure shown, find the value of frictional force between $A$ & $B$ and $B$ and the surface respectively. Take $g=10{\text{m/s}}^2$.

A block of mass m is placed on a wedge. The wedge can be accelerated in four manners marked as (1), (2), (3) and (4) as shown. If the normal reactions in situation (1), (2), (3) and (4) are $N_1,N_2,N_{3}and{N}_4$ respectively and acceleration with which the block slides on the wedge in situations are $b_1,b_2,b_{3}and{b}_4$ respectively then:

A spherical shell at rest at the origin explodes into three fragments of masses 1 kg, 2 kg and 'm' kg. The 1 kg and 2 kg pieces fly off with speeds of $12m{s}^{-1}$ along the x-axis and 8 $m{s}^{-1}$ along the y-axis respectively. If the 'm' kg piece flies off with a speed of 40 $m{s}^{-1}$ , the total mass of the shell must be

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to

A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is

Find the minimum value of '$m$', for the sytem to be in equilibrium. Take $g=10m/s^2$.

A scale which is calibrated at ${10}^{\circ }\text{C}$ measures the length of a stick to be $60\text{cm}$, at temperature ${30}^{\circ }\text{C}$ . If thermal coefficient of linear expansion of the rod is $2\times {10}^{-5}{/}^{\circ }\text{C}$, the correct length of the stick in $\text{cm}$ is:

Statement I : Rays incident on a convex mirror from a point source of light, after reflection diverge.

Statement II : A convex mirror can never form a real image for a point source of light.

If the earth stops rotating, the apparent value of g on its surface will

For a certain organ pipe, three successive resonance frequencies are observed at $425\text{Hz}$, $595\text{Hz}$ and $765\text{Hz}$ respectively. The fundamental frequency of the pipe is -

$[$speed of sound in air $=340\text{m/s}]$

A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let $v_P,v_{Q}and{v}_C$ be the magnitude of velocities of points P,Q and C respectively, then

A person with a mass of $M\text{kg}$ stands in contact against the wall of a cylindrical drum of radius $r$ rotating with an angular velocity $\omega$. If the coefficient of friction between the wall and the clothing is $\mu$, the minimum rotational speed of the cylinder which enables the person to remain stuck to the wall when the floor is suddenly removed, is

The number of possible modes of natural oscillations of air column in a pipe closed at one end of length $170\text{cm}$ below frequency $1450\text{Hz}$ are

[velocity of sound $=340{\text{ms}}^{-1}$]

A disc of mass $M$ radius $R$ is fixed about an axis as shown in figure. If a particle of mass $\frac{M}{4}$ moving with speed $v$ perpendicular to the disc plane, hits the disc at point $P$ and sticks to the disc, the disc starts rotating about its axis as shown. Find the angular velocity of the system (disc + particle) after the hit.

The potential energy of a particle of mass $1\text{kg}$ moving along the $X$-axis is given by $U=4(1+\cos 2x)\text{J},$ where $x$ is in meters. Find the time period of small oscillation (in second).

A very small hole is made at the bottom of a tank filled with water (density $=1000{\text{kg/m}}^3$). If the total pressure at the bottom of the tank is $3\text{atm}$ $(1\text{atm}={10}^5{\text{N/m}}^2)$, then the velocity of efflux is:

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

A particle is thrown at angle $\theta$ with horizontal over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If $\alpha$ and $\beta$ be the base angles, find $\tan \alpha +\tan \beta$.

If the mean free path of atoms is doubled then the pressure (P) of gas will become

A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be

A block of mass $2\text{kg}$ slides down an incline plane of inclination ${30}^{\circ }$. The coefficient of friction between block and plane is $0.5$. The contact force between block and incline plane is :

The forward biased diode connection is:

The bulk modulus of rubber is $9.8\times {10}^8{\text{N/m}}^2$. To what depth a rubber ball must be taken in a lake so that its volume is decreased by $0.1\%$?

(Neglect atmospheric pressure)

From a tap $10m$ high, water drops fall at regular intervals. When the first drop reaches the ground, the $5^{th}$ drop is about to leave the tap. Find the separation between $2^{nd}$ and $3^{rd}$ drops.

Two particles of the same mass are projected from the ground with the same speed $10\text{m/s}$ at an angle ${37}^{\circ }$ and ${53}^{\circ }$ with the horizontal respectively. Find out the maximum height attained by their $COM$. $(g=10{\text{m/s}}^2)$

A car starting from rest accelerates at the rate $f$ through a distance $s$, then continues at constant speed for time $t$ and then decelerates at rate $\frac{f}{2}$ to come to rest. If the total distance covered is $15s$, then which one is correct?

On the Celsius scale the absolute zero i.e. $0^{\circ }K$ is equal to_____.

A block of mass M has a circular cut with a frictionless surface as shown. The block rests on the horizontal frictionless surfaced of a fixed table. Initially the right edge of the block is at x = 0, in a coordinate system fixed to the table. A point mass m is released from rest at the topmost point of the path as shown and it slides down. When the mass loses contact with the block, its position is x and the velocity is v. At that instant, which of the following option is/are correct ?

Two spheres of mass $2\text{kg}$ and $6\text{kg}$ are moving with velocities $4\text{m/s}$ and $8\text{m/s}$ away from each other along the same line. The ball of mass $2\text{kg}$ is moving towards left. The velocity of the center of mass is

The unit vector along $\overrightarrow{A}\times \overrightarrow{B}$ is

The energy produced by the Sun largely involves which of the following nuclei?

A circular plate of uniform thickness has a diameter of $28\text{cm}$. A circular portion of diameter $21\text{cm}$ is removed from the plate as shown. $O$ is the centre of mass of complete plate. The position of centre of mass of remaining portion will shift towards left from $O$ by

Refractive index for a material for infrared light is

[CPMT 1984]

A wheel rotates with a constant angular acceleration of $3.6{\text{rad/s}}^2$. If angular velocity of the wheel is $4.0\text{rad/s}$ at time $t_0=0$, what angle does the wheel rotate in $1\text{s}$? What will be its angular velocity at $t=1\text{s}$?

The trajectory of a projectile in a vertical plane is given by $y=ax-b{x}^2,$ where $a$ and $b$ are constants and $x$ and $y$ are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the particle and the angle of projection from the horizontal are

Identify "Periodic Motion”?

A body can be negatively charged by

A particle moves along parabolic path $x=y^2+2y+2$ in such a way that $y-$ component of velocity is constant and equal to $5\text{m/s}$ during the motion. Magnitude of acceleration of the particle

The adjoining diagram shows the spectral energy density distribution $E_{\lambda }$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16:1$, the value of temperature $T$ is

The initial velocity of a particle is $10\text{m/sec}$ and its retardation is $2{\text{m/sec}}^2$. The distance covered in the fifth second of the motion will be

Mass $M$ is distributed uniformly along a line of length $2L$. A particle of mass $m$ is at a point ($\text{P}$) at distance $a$ above the centre of the line on its perpendicular bisector as shown in figure. The gravitational force that the mass distribution along the line exerts on the particle is

A quarter circular conducting ring of radius $r$ is rotating at angular velocity $\omega$ in uniform magnetic field as shown in figure.

EMF induced across the ring is

A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r’, then the critical angle will be

Which of the following options represent a travelling wave? Here, $y$ is the displacement of the particle, $x$ is the position of the particle from origin and $t$ is time.

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 $II$

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) Work done on block by gravity}& \text{(p)}144\text{J}\\ \text{(b) Work done on block by normal reaction}& \text{(q)}32\text{J}\\ \text{(c) Work done on block by friction}& \text{(r)}56\text{J}\\ \text{(d) Work done on block by all the forces}& \text{(s)}48\text{J}\\ & \text{(t)}\text{None}\end{array}$