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Figure shows a smooth track, a part of which is a circle of radius $r$. A block of mass $m$ is pushed against a spring of spring constant $k$ fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force $mg$ when it reaches the point $P$, where the radius of the track is horizontal.

A parallel beam of light ray parallel to the X-axis is incident on a parabolic reflecting surface $x=2b{y}^2$ as shown in the figure. After reflecting it passes through focal point F. The focal length of the reflecting surface is :

Two different adiabatic paths for the same gas intersect two isothermal $T_{1}and{T}_2$ _­as shown in the P-V diagram. Then $V_a/V_d$ is equal to

The inductance of a solenoid is $5\text{H}$ and its resistance is $5\Omega$. If it is connected to a $10\text{Volt}$ battery, then time taken by the current to reach ${\frac{9}{10}}^{th}$ of its maximum will be

The interference pattern is obtained by two coherent sources of same intensities $I_0$. Find intensity at $y=\frac{D\lambda }{6d}$ from central maximum.

A turn table is rotating about the fixed vertical axis. A particle of mass $m$ is lying on a table at rest with respect to the table. An observer is standing over a block of mass $M$ moving with an acceleration $a$. Find the magnitude of pseudo-force on a particle of mass $m$ as observed by the observer. (Given a body is subjected to an acceleration called centripetal acceleration directed towards the centre when it is rotating and is equal to $r{\omega }^2$ )

Figure shows a system of three concentric metal shells A, B and C with radii, a, 2a and 3a respectively. Shell B is earthed and shell C is given a charge Q. Now, if shell C is connected to shell A, then the final charge on the shell B, is equal to

A sample of 8 gram of Helium is heated from ${27}^{\circ }C$ to ${327}^{\circ }C$, find ratio of heat added to work done by gas during process

A heavy nucleus having mass number $200$ gets disintegrated into two small fragments of mass number $80$ and $120$. If binding energy per nucleon for parent atom is $6.5MeV$ and for daughter nuclei is $7MeV$ and $8MeV$ respectively, then the energy released in the decay will be:

Two similar plano-convex lenses are placed with their convex surfaces in contact and the space between them is filled with a liquid of refractive index $1.7$, as shown in figure. The focal length of plano-convex lens is $25cm$ and radius of curvature of the curved surface is $12.5cm$. The focal length of the combination is :

A thin glass rod is bent into a semicircle of radius r. A charge +Q is uniformly distributed along the upper half and a charge -Q is uniformly distributed along the lower half as shown in the figure. The electric field E at P, the centre of the semicircle, is

A block of mass $m$ is constrained to move inside a ring of radius $R$ which is fixed on a horizontal smooth table. At time $t=0$, block is moving along the inside of the ring (i.e., in the tangential direction) with velocity $v_0$. The coefficient of friction between the block and the ring is $\mu$. Then the speed of the block at time $t$ is

Potentiometer wire AB has length = 100 cm. Total resistance of wire is 10$\Omega$, when the jockey is connected at D (AD = 10x cm), ammeter reading is 0.5 amp. Value of x is. (Resistance of ammeter is $1\Omega$ and the cell has no internal resistance).

From the graph between current (I) and voltage (V) shown below, identify the portion corresponding to negative resistance

Two soap bubbles, one of radius $50mm$ and the other of radius $80mm$, are brought in contact so that they have a common interface. The radius of the curvature of the common interface is

An open pipe is suddenly closed at one end and with the result frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. What is the fundamental frequency of the open pipe?

A railway carriage box has its geometric centre (i.e we will assume the force due to gravity to act at this point) at a height of $1\text{m}$ above the rails, which are $1.5\text{m}$ apart. The maximum safe speed at which it could travel round an unbanked curve of radius $100\text{m}$ is

An object is placed beyond the principal focus at a distance of $9\text{cm}$ from it in front of a concave mirror on the principal axis. The image is formed beyond the principal focus at a distance of $16\text{cm}$ from the principal focus. The focal length of the mirror is

A block of 4 kg mass starts at rest and slides a distance d down a friction less incline (angle ${30}^{\circ }$) where it runs into a spring of negligible mass. The block slides an additional 25 cm before it is brought to rest momentarily by compressing the spring. The force constant of the spring is $400N{m}^{-1}$. The value of d is (take $g=10m{s}^{-2}$)

A small solid sphere of radius R made of a material of bulk modulus B is surrounded by an incompressible liquid in a cylindrical container. A massless piston of area A floats on the surfaces of the liquid. Find the magnitude of fractional change in the radius of the sphere $\left(\frac{dR}{R}\right)$ when a mass M is placed slowly on the piston to compress the liquid.

A chain of mass per unit length $\lambda =2\text{kg/m}$ is pulled up by a constant force $F$. Initially, the chain is lying on a rough surface and passes onto the smooth surface. The co-efficient of kinetic friction between chain and rough surface is $\mu =0.1$. The length of the chain is $L$. Then, find the speed ($\text{in m/s}$) of the chain when $x=L$. Take $g=10{\text{m/s}}^2$.

Two sinusoidal plane waves of the same frequency having intensities $I_0$ and $4I_0$ are travelling in the same direction. The resultant intensity at a point at which the waves meet with a phase difference of $\frac{\pi }{2}$ is

A particle is aimed at a mark which is in the same horizontal plane as that of the point of projection. It falls $10m$ short of the target when it is projected with an elevation of ${75}^{\circ }$ and falls $10m$ ahead of the target when it is projected with an elevation of ${45}^{\circ }$. If $\theta$ is the correct elevation so that it exactly hits the target, find the value of $\sin 2\theta$ (for the same velocity of projection)

Flux $\varphi$ (in $weber$) in a closed circuit of resistance $10\Omega$ varies with time $t$ (in $seconds$) according to the equation $\varphi =6t^2–5t+1$. What is the magnitude of the induced current at $t=0.25s$?

A convex lens produces a double size real image when an object is placed at a distance of 18 cm from it. Where should the object be placed to produce a triple size real image ?

Find the moment of inertia for hollow sphere and solid sphere.

Note: (need solution step by step with clear imagine and solve in easy method)

Difference between precise and accurate measurement.

How to calculate the gravitational field due to a point mass?

A ball rolls off the top of a staircase with velocity u m/s . If the steps are h metre high and b metre wide, the ball will hit the edge of nth step, when

A river flows due south with a speed of 2.0 m/s. A man steers a motorboat across the river; his velocity relative to the water is 4 m/s due east. The river is 800 m wide. How far south of his starting point will be reach the bank?

An elevator is descending with uniform acceleration . to measure the acceleration a person in the elevator drops a coin at the moment the elevator starts .The coin is 6ft above the floor of the elevator at the time it is dropped . The person observes that the point strikes the floor in 1s. Calculate from these data the acceleration f the elevator.

If the universe were shrunk to the size of the earth , how large earth would be on this scale?

A tank is filled upto height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get maximum range $x_m$, a small hole is punched at a distance $y$ from the free surface of the liquid. Then find the value of maximum range ($x_m$).

The displacement of a particle varies with time as $x=12\sin \omega t-16{\sin }^3\omega t\left(\text{in cm}\right)$. If the particle is executing S.H.M, then its maximum acceleration is

As shown in the figure a ball of mass $m$ hits a floor with a speed $u=10\sqrt{2}\text{m/s}$ making an angle of incidence $\alpha ={45}^{\circ }$ with the normal. The coefficient of restitution is $e=0.5$. Find the speed of the reflected ball and the angle of the reflection.

A particle is revolving in a circular path having radius $‘r^{\prime }=1m$ at a speed of $2m/s$. It is increasing its speed at the rate of $3m/s^2$. The magnitude of total acceleration of the particle at that instant is

A thief with a stolen car passes through a police check post at his top speed of 90 km per hour a motorcycle cop reacting after 2 seconds accelerates from rest at 5 metre per second square is top speed being 108 km per hour find the maximum separation between police man and thief

A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the wrath once in 8 days. The radius of the orbit of the of the second satellite is?

A boy standing at top of a tower of 20 m height drops a stone. Assuming g=10m/S2. The velocity with which it hits the ground is???

A car moves on a horizontal track of radius $r$, the speed is increasing at a constant rate $a$, coefficient of friction between road and tyre is $\mu ,$ the speed at which car will skid is

The volume of a glass vessel is 1000 cc at ${20}^{\circ }C$. What volume of mercury should be poured into it at this temperature so that the volume of the remaining space does not change with temperature ? Coefficients of cubical expansion of mercury and glass are $1.8\times {10}^{-4}{}^{\circ }{C}^{-1}$ and $9.0\times {10}^{-6}{}^{\circ }{C}^{-1}$ respectively.

Photoelectric work function of a metal 1 eV. If a light of wavelength 500 Å falls on the metal, the speed of the photoelectron emitted approximately will be- (h = 6.625 × ${10}^{–34}$ J s)