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The wave number of the radiation whose quantum is $1erg$ is

A particle of mass 10 grams is executing simple harmonic motion with an amplitude of 0.5 m and periodic time of (π/5) seconds. The maximum value of the force acting on the particle is

[MP PET 1999; MP PMT 2000]

Nature of meniscus for liquid of $0^{\circ }$ angle of contact

A motor cycle engine delivers a power of $10\text{kW}$ by consuming petrol at the rate of $2.4\text{kg/hr}$. Find the rate of heat rejection by the exhaust, if the calorific value of petrol is $35.5\text{MJ/kg}$.
(Neglect the other losses)

Two waves having same amplitude $\left(A\right)$, wavelength $\left(\lambda \right)$ and frequency $\left(f\right)$ are propagating in the same direction. They interfere such that the amplitude of resultant wave is zero. The path difference between two wave can be :

A 2 kg block is placced over a 4 kg block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is 0.20. Find the acceleration of the two blocks if a horizontal force of 12 N is applied to (a) the upper block, (b) the lower block. Take $g=10m/s^2$

A gasoline engine takes in 5 moles of air at ${20}^{\circ }$ C and 1 atm, and compresses it adiabatically to ${\frac{1}{10}}^{th}$ of the original volume. Find the change in internal energy. (Assume air to be diatomic)

For the arrangement as shown in the figure, the maximum force F, for no relative motion between block is

A uniform vertical cylinder of cross-sectional area A floats, 90 $\%$ submerged in an unknown liquid inside a tank with cross-sectional area four times that of cylinder When cylinder is pushed down gently by x , the liquid comes up by $x_1$ w.r.t. the original level. Then the ratio of x to $x_1$ will be________.

In a metre bridge, the gaps are closed by two resistances P & Q & the balance point is obtained at 40 cm. when Q is shunted by a resistance of $10\Omega$, the balance point shifts to 50 cm. the values of P & Q are

respectively

A block of mass $3\text{kg}$ is suspended from a spring of constant $150\text{N/m}$. The block is released when the spring is at natural length. Match the extension in the spring with the description in List-II.
Assume that in all the options the block is moving downwards.

$\begin{array}{cccc}& \text{Column -I}& & \text{Column-II}\\ \text{(A)}& \text{20 cm}& \text{(P)}& \text{Speed is zero but acceleration is maximum in magnitude}\\ \text{(B)}& \text{40 cm}& \text{(Q)}& \text{Speed is increasing and acceleration is decreasing in magnitude}\\ \text{(C)}& \text{30 cm}& \text{(R)}& \text{Speed is decreasing and acceleration is increasing in magnitude}\\ \text{(D)}& \text{10 cm}& \text{(S)}& \text{Speed is maximum but acceleration is zero in magnitude}\end{array}$
Which of the following is the only CORRECT combination ?

A mass m supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration with the mass fall on release?

At a certain place the horizontal component of earth's magnetic field is $\sqrt{3}$ times the vertical component. The angle of dip at that place is

A tuning fork vibrating with a sonometer having $20cm$ wire produces $5$ beats per second. If the beat frequency does not change if the length of the wire is changed to $21cm$, then the frequency of the tuning fork $($in $Hz)$ must be

The rate of emission of radiation of a black body at ${273}^{\circ }C$ is $E$, then the rate of emission of radiation of this body at $0^{\circ }C$ will be

A tank containing water has an orifice on one vertical wall. If the centre of the orifice is 5 m below the surface of water in the tank, the velocity of discharge is (take g = 9.8 m/s²)

Two blocks of masses $M_1$ and $M_2$ are connected with a string passing over a pulley as shown in the figure. The block $M_1$ lies on a horizontal surface. The coefficient of friction between the block $M_1$ and the horizontal surface is $\mu$. The system accelerates. What additional mass $m$ should be placed on the block $M_1$ so that the system does not accelerate?

Two points are moving with simple harmonic motions of same period and amplitude along the same line. They are found to cross each other in opposite directions, always at the point for which the displacement $x=\frac{A}{2}$, where A is the amplitude. Find the “phase difference” between the two motions.

Two cells with the same emf E and different internal resistance $r_{1}and{r}_2$, are connected in series to an external resistance R. The value of R so that the pd across the first cell is zero, is:

A telescope has a objective of focal length $50cm$ and an eye-piece of focal length $5cm$. The least distance of distinct vision is $25cm$. The telescope is focused for distinct vision on a scale of $200cm$ away. The separation between the objective and the eye-piece is

When photons of wavelength ${\lambda }_1$ are incident on a metal plate, the corresponding stopping potential is found to be $V$. When photons of wavelength ${\lambda }_2$ are used, the corresponding stopping potential was thrice the above value. If light of wavelength ${\lambda }_3$ is used, the stopping potential for wavelength ${\lambda }_3$ in terms of ${\lambda }_1$ and ${\lambda }_2$ will be

A ring of mass $m$ and radius $R$ is rotating with angular speed $\omega$ about a fixed vertical axis passing through it's centre $O$ with two point masses each of mass $\frac{m}{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of the system is
$\frac{8}{9}\omega$ and one of the masses is at a distance of $\frac{3}{5}R$ from $O$. At this instant the distance of the other mass from $O$ is

In a galvanometer 5% of the total current in the circuit passes through it and remaining through shunt. If the
resistance of the galvanometer is G, the shunt resistance S connected to the galvanometer is

A simple pendulum of length $l$ is displaced so that its taught string is horizontal and then released. A uniform bar pivoted at one end is simultaneously released from its horizontal position. If their motions are synchronous, what is the length of the bar?

A planet of mass M, has two natural satellites with masses $m_1$ and $m_2$. The radii of their circular orbits are $R_1$ and $R_2$ respectively. Ignore the gravitational force between the satellites. Define $v_1,L_1,K_1$ and $T_1$ to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite $1$; and $v_2,L_2,K_2$ and $T_2$ to be the corresponding quantities of satellite $2$. Given $m_1/m_2=2$ and $R_1/R_2=1/4$, match the ratios in List - I to the numbers in List-II.

A spring of unstretched length $l$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

Two blocks tied with a massless string of length $3\text{m}$ are placed on a table rotating at an angular speed $\omega =4\text{rad/s}$. The axis of rotation is $1\text{m}$ from the block having $1\text{kg}$ mass. Assume that the surface below $2\text{kg}$ block is smooth and that below the $1\text{kg}$ block is rough. Find the tension $\left(T\right)$ in the string and the frictional force$\left(f\right)$ acting on the $1\text{kg}$ block. Take $g=10{\text{m/s}}^2$

A block of mass $5\text{kg}$ is resting on a rough horizontal surface. Now a force of $24N$ is imparted to it with a negligible impulse as shown in the figure. If the coefficient of kinetic friction is 0.4 and $g=10{\text{m/s}}^2$, then the acceleration of the block will be

If a straight line in space is equally inclined to the co-ordinate axes, the cosine of its angle of inclination to any one of the axes is
[MP PET 1992]

A tank full of water has a small hole at its bottom. Let $t_1$ be the time taken to empty first half of the tank and $t_2$ be the time needed to empty rest half of the tank, then

A light rod of length $l$ has two masses $m_1$ and $m_2$ attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is

Metallic sphere of radius $5cm$ is surrounded by air. Dielectric strength of air is $5\times {10}^{5}V/m$ , then maximum charge that can be placed on sphere is

An electron (mass $m$) with an initial velocity, $\overrightarrow{v}=v_0\hat{i}(v_0>0)$ is in an electric field, $\overrightarrow{E}=-E_0\hat{i}(E_0=\text{constant}>0)$ . Its de broglie wavelength at time $t$ is given by (${\lambda }_0$ is the initial wavelength of electron)

A steel wire of uniform cross - sectional area $2m{m}^2$ is heated up to ${50}^{\circ }$ C and is stretched by clamping its two ends rigidly. The change in tension when the temperature falls from ${50}^{\circ }$ C to ${30}^{\circ }$C is given by:
$\alpha =1.1\times {{10}^{-5}}^{\circ }C,Y=2.0\times {10}^{11}\frac{N}{m^2}$

A neutral particle is initially at rest in a uniform magnetic field B as shown in the diagram. The particle then spontaneously decays into
two fragments, one with a positive charge +q and mass 3m and the
other with a negative charge –q and mass m. Neglecting the
interaction between the two charged particles and assuming
that the speeds are much less than speed of light, the time
after the decay at which the two fragments first meet is [Data :
$q=1\mu C,B=2\pi \mu T,m={10}^{–15}kg$ Both the charges have initial velocities in x-y plane]

Consider a slab of varying RI as shown in figure. If width of slab is very large, then maximum possible y- co-ordinate of light ray where it will escape: (where yis in meter)

A solid sphere of mass $m$ is released from rest from the rim of a hemispherical cup so that it rolls along the surface. Find the normal contact force between the solid sphere and the cup at the bottom most point.

The velocity of water near the surface of river is 5 m/s whereas the depth is 5m. The coefficient of viscosity of water is ${10}^{-2}$ poise, then shearing stress will be

A thread is tied slightly loose to a wire frame as in figure and the frame is dipped into a soap solution and taken out the frame is completely covered with the film. When the portion ‘A’ is punctured with a pin, the thread

A body is sliding down an inclined plane having coefficient of friction 0.5. The normal reaction is twice that of resultant downward force along the inclined plane. The angle between the inclined plane and the horizontal is..

Figure shows two small blocks placed on a smooth horizontal surface. They start moving from the same line with force $2F$ and $F$ respectively acting on the blocks. Their momenta and kinetic energies at the instants of crossing the finishing line as shown in figure are $p_A,p_B$ and $K_A,K_B$. Then choose the correct option.