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A body of mass 6 kg collides with another body at rest. After the collision, they travel together with a velocity that is one third of the initial velocity of 6 kg mass. The mass of the second body is

Three discs of the same mass and same radius $R$ are placed as shown in figure. Find the $COM$ of the system.

A hoop of mass 'm' and radius 'R' is projected on a floor with linear velocity $v_0$ and reverse spin ${\omega }_0$. The coefficient of friction between the hoop and the ground is $\mu$. Under what of the following condition will the hoop return back?

A particle of mass $M$, starting from rest, undergoes uniform acceleration. If the speed acquired in time $T$ is $V$, the average power delivered to the particle is

A charge q is located above the centre of a square plate of side a, at a distance $\frac{a}{2}$. The flux of electric field through the plate Is?

A particle starts from rest. Its acceleration at time $t=0$ is $5{\text{ms}}^{-2}$ which varies with time as shown in figure. The maximum speed of the particle will be

A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.

The value of inductance L is

The load versus elongation graph for four wires made of the same material and having the same length is shown in the figure. The thickest wire is represented by the line

Two ideal springs of different lengths have been suspended from points $A$ and $B$ such that their free ends $C$ and $D$ are at the same horizontal level. A massless rod $PQ$ is attached to the ends of the springs. A block of mass $m$ is attached to the rod at point $R$. The rod remains horizontal in equilibrium. Now, the block is pulled down and released. It performs vertical oscillations with time period $T=2\pi \sqrt{\frac{m}{3k}}$ where $k$ is the force constant of the longer spring.





Find the ratio of lengths $RC$ and $RD$.

The given infinite grid consists of hexagonal cells of six resistors each of resistance R. Then $R_{12}$ is equal to

A block of mass m slides with a speed of $v_0=6\text{m/s}$ along a track from one level to a heigher level as shown. The track is frictionless until the block reaches the higher level where co-efficient of friction is $0.6$. The distance $d$ travelled by block on higher level before stopping is $(g=10{\text{m/s}}^2)$

Which of the following graphs correctly represents the variation of speed of sound with temperature in a particular gas?

Ratio of the weights of a $1\text{kg}$ block of iron and $1\text{kg}$ block of wood as measured by a spring balance is:

Given: Density of iron $=7800{\text{kg/m}}^3$, density of wood $=800{\text{kg/m}}^3$ and density of air $=1.293{\text{kg/m}}^3$

Four persons $A,B,C$ and $D$ at the corners of a square of side $X$ start moving at a constant speed $V$. Each person maintains a direction towards the person at the next corner. The time the persons take to meet each other is

A thin uniform circular disc of mass $M$ and radius $R$ is rotating with an angular velocity $\omega ,$ in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same dimensions but of mass $\frac{M}{4}$ is placed gently on the first disc co-axially. The final angular velocity of the system is

Two sources of sound $\text{A}$ and $\text{B}$ produce waves of $350\text{Hz}$. The particle at point $\text{P}$ is vibrating under the influence of these two waves. The amplitudes of the two waves are $0.3\text{mm}$ and $0.4\text{mm}$. If $AP-BP=25\text{cm}$ and velocity of sound is $350\text{m/s}$, the resultant amplitude of the particle at point $\text{P}$ will be

A carbon resistance is having a followingcoding green, orange, black and gold. Its resistance is

A one-litre flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in the flask? Given the coefficient of linear expansion of glass is $9\times {10}^{-6}{}^{\circ }{C}^{-1}$ and the coefficient of volume expansion of mercury is $1.8\times {10}^{-4}{}^{\circ }{C}^{-1}$

A $20\text{N}$ metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads $40\text{N}$. The spring balance is now lowered slowly into the beaker such that the block gets immersed in the water. The spring balance now reads $16\text{N}$. The reading of the weighing machine will be

A particle is projected with certain velocity at an angle $\alpha$ above the horizontal from the foot of an inclined plane having inclination of ${30}^{\circ }$. If the particle strikes the plane normally then $\alpha$ is:

A thin square plate of side $3\text{m}$ has mass $5\text{kg}$. Find the moment of inertia about axis $AB$ as shown in figure.

An object is moving in a circle of radius 100 m with a constant speed of 31.4 m/s. What is its average speed for one complete revolution

A ball is projected with kinetic energy E at an angle of ${45}^{\circ }$ to the horizontal. At the highest point during its flight, its kinetic energy will be

An object is gently placed on a long conveyer belt moving with a uniform speed of $5m{s}^{-1}$. If the coefficient of friction between the block and the belt is 0.5, how far will the box move on the belt (relative to belt) before coming to rest? Take $g=10m{s}^{-2}$.

A $1\text{kg}$ ball is released and slides down from point $\text{A}$ to point $\text{C}$, as shown in the figure below. If the acceleration due to gravity$=10\text{m}/s^2$, the kinetic energy of the ball when it arrives at point $\text{C}$.

A solid sphere of radius R is set into motion on a rough horizontal surface with a linear speed $v_0$ in forward direction ad an angular velocity ${\omega }_0=\frac{v_0}{2R}$ in counter clockwise direction as shown in figure. If co-efficient of friction is $\mu$, then find

(i)The time after which sphere starts pure rolling,

(ii)The work done by friction over a long time

A body X with a momentum p collides with another identical stationary body Y one dimensionally. During the collision, Y gives an impulse J to body X. Then coefficient of restitution is

By what percentage should the pressure of a given mass of gas be increased so as to decrease its volume by 10$\%$ at a constant temperature?

A metallic wire of length L metres extends by l metres when stretched by suspending a weight Mg to it. The mechanical energy stored in the wire is

A body at rest may have

Consider the following two statements

1.Linear momentum of a system of particles is zero

2.Kinetic energy of a system of particles is zero

Then

A flag is hoisted on the steamer boat.On the basis of the data given below find out the direction of flutter of

the flag

${\overrightarrow{v}}_{steamer/water}=10\sqrt{3}m{s}^{-1}$ towards North

${\overrightarrow{v}}_{water}=5m{s}^{-1}$ towards East

${\overrightarrow{v}}_{wind}=5m{s}^{-1}$ towards East

(Assume the wind does not affect the steamer)

Find the M.O.I $\left(I\right)$ of a uniform solid sphere of radius $R$ and mass $M$ about its tangent

What is the minimum value of the refractive index for a ${90}^{\circ }–{45}^{\circ }–{45}^{\circ }$ prism

which is used to deviate a beam through ${90}^{\circ }$ by total internal reflection ?

A light source lies at the angle bisector of two plane mirrors inclined at an angle of $\theta$. The limitation for the value of $\theta$ so that the light reflected from one mirror does not reach the other mirror will be

What is the equivalent spring constant for the syatem shown below in the figure?

(All the springs are ideal and identical having spring constant $k\text{N/m}$)

A simple pendulum is released from $A$ as shown. If $M$ and $l$ represent the mass of the bob and length of the pendulum respectively, the gain in kinetic energy at B is

Figure shows a combination of logic gates. To what single gate is this combination equivalent?

A block of mass 250 g is kept on a vertical spring of spring constant 100 N/m fixed from below. The spring is now compressed to have a length 10 cm shorter than its natural length and the system is released from this position. How high does the block rise from this position? Take g = 10 m/$s^2$.

One end of a cylindrical glass rod shown in figure ends in a hemispherical surface of radius R = 20 mm.

-Let the same rod be immersed in water of index 1.33, the other quantities having the same values as before. Find the image distance.

A series LCR circuit containing a resistor of $120\Omega$ has an angular resonant frequency $4\times {10}^{5}rad{s}^{-1}$. At resonance the voltages across resistor and inductor are 60 V and $40\text{V}$ respectively.

The value of capacitance C is

A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are $18\text{cm}$ and $16\text{cm}$ respectively. The minimum possible length of the string is:

A rod $OA$ of mass $m$ and length $L$ is rotating in a horizontal circle about point $O$ as shown in figure. $B$ is the mid-point of rod. If $T$ represents tension in the rod at any point and $U_o$ represents elastic strain energy stored in the rod $OA$, $U_B$ represents elastic strain energy stored in the rod $\left(OB\right)$ then choose correct alternative (s).

On a hot day in Jaipur, an oil trucker loaded 40 kL (kilolitres) of diesel fuel. On his way to Shimla, he encounters a temperature drop of ${20}^{\circ }C$, where he stopped and delivered the entire load. How many litres did he deliver? The γ for diesel is $9.50\times {10}^{-4}{/}^{\circ }C$ and α for his steel truck is $11\times {10}^{-6}{/}^{\circ }C$. If you find that the volume has decreased, think about who is paying for the "missing” diesel.

The energy radiated by a black body at $2300\text{K}$ is found to have a maximum intensity at a wavelength $1260\text{nm}$, its emissive power being $8000{\text{W/m}}^2$. When the body is cooled to a temperature $T\text{K}$, the emissive power is found to decrease to $500{\text{W/m}}^2$. Find the temperature $T$.

A body travelling along a straight line traversed one third of the total distance with a velocity $4\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity averaged over the whole time of motion is