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Two blocks are placed on a wedge with coefficients of friction being different for two blocks.Choose the correct option (friction is not sufficient to prevent the motion)

A ball is dropped from a height. If the maximum percentage errors in measurement of the height and the time are $e_1$ and $e_2$ respectively, then maximum percentage error in the estimation of $g$ is

In $LC$ circuit the inductance $L=40\text{mH}$ and capacitance $C=100\mu \text{F}.$ If a voltage $V\left(t\right)=10\sin \left(314t\right)$ is applied to the circuit, the current in the circuit is given as

A solid sphere of mass M and radius R having a moment of inertia I about its diameter is recast into a solid disc fo radius r and thickness t. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains I. Then R and r are related as

A Charged sphere of mass $m$ and charge $q$ starts sliding from rest on a vertical fixed circular track of radius $R$ from the position as shown in figure. There exists a constant magnetic field in horizontal direction as shown in figure. The maximum force exerted by track on the sphere is:

The magnetic field $B$ at a distance $r$ from a long straight wire carrying current varies with distance $r$ as shown in the figure.

A transverse wave having amplitude $A=\frac{4}{\pi }\text{m}$ and frequency $f=2\text{Hz}$ is travelling on a string of linear mass-density $\mu =1\text{kg/m}$. If the total kinetic energy associated with one wavelength of the wave is $16\text{J}$. Then the wavelength of the transverse wave is

The contents of a well-insulated tank are heated by a resistor of 23 $\Omega$ in which 10 a current is flowing. Consider the tank along with its contents as a thermodynamic system. The work done by the system and the heat transfer to the system are positive. The rates of heat (Q). work (W) and change in internal energy (\Delta U) during the process in kW are

A boy takes $90$ second to walk up a stalled escalator. However, if the escalator is moving and he stands on the escalator, he is carried up in one minute. how much time the boy would take to walk up the moving escalator?

At t = 0, a transverse wave pulse in a wire is described by the function
$y=\frac{6}{(x^2-3)}$ where x and y are in metres. The function y(x, t) that describes this wave equation if it is travelling in the positive x direction with a speed of 4.5 m/s is

Dip angle increases from ${30}^{\circ }$ to ${60}^{\circ }$ at a place if vertical plane in which needle is suspended is rotated by angle $\alpha$ from magnetic meridian. Then $\alpha$ is.

The speed of an electron having a wavelength of the order of $1\stackrel{\circ }{A}$ will be

A current loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations in magnetic field B as shown in the figures below:

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in

(i) stable equilibrium and

(ii) unstable equilibrium?

The total energy of a particle executing S.H.M. is proportional to

[CPMT 1974, 78; EAMCET 1994; RPET 1999;

MP PMT 2001; Pb. PMT 2002; MH CET 2002]

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed at point $\text{O}$. If there is a vertical magnetic field $B$ in the region, the e.m.f induced across the ends of the rod is:

A ball is made of a material of density $\rho$ where, ${\rho }_{\text{oil}}<\rho <{\rho }_{\text{water}}$ with ${\rho }_{\text{oil}}$ and ${\rho }_{\text{water}}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium positions?

A man is approaching a plane mirror with constant acceleration of 4 $m/s^2$. Initially the person is at rest. Mirror is moving towards the person with a constant velocity of 4 m/s. The correct variation of velocity of image of man (wrt ground) vs time is best given by consider leftwards as positive)

The figure below is a representation of a simple harmonic progressive wave, progressing in the negative X- axis, at a given instant. The direction of the velocity of the particle at state P in the figure is best represented by the arrow.

Two blocks of masses $m_1$ and $m_2$ are connected with a light spring of force constant $k$ and the whole system is kept on a frictionless horizontal surface. The masses are applied forces $F_1$ and $F_2$ as shown in figure. At any time, the blocks have same acceleration $a_0$ but in opposite directions.

Then acceleration $a_0$ is

For given conducting shells equivalent capacitance between A & B is

The magnetic dip angle at two places are ${30}^{\circ }$ and ${45}^{\circ }$. The ratio of horizontal components of earths magnetic field at the two places is-

A cell of internal resistances $r$ is connected to a load of resistance $R$. Energy is dissipated in the load, but some thermal energy is also wasted in the cell. The efficiency of such arrangement is found from the expression



$\frac{\text{Energy dissipated in the load}}{\text{Energy dissipated in the complete circuit}}$



Which of the following gives the efficiency in this case?

Shape of a transverse wave at time $t=t_0$ is shown in the figure given below.

At $x=x_0$ and time $t=t_0$, slope of the wave curve is $5$. Find the ratio of particle velocity to the wave velocity at $x=x_0$.

If threshold frequency of a metal surface is $7\times {10}^{14}\text{Hz}$, find the work function of the metal.

A motorcyclist wants to drive on the vertical surface of a wooden well of radius $5\text{m}$, with a minimum speed of $5\sqrt{5}{\text{ms}}^{-1}$. The minimum value of coefficient of friction between the tyres and the wall of the well must be

$($Take, $g=10{\text{ms}}^{-2})$

A monoatomic gas undergoes an adiabatic process as indicated in the given figure. Find the work done during the process.

A solid sphere of mass $2\text{kg}$ and radius $1\text{m}$ is performing combined rotational and translational motion as shown in figure. Find the total kinetic energy of the solid sphere.

In a fillet weld, the direct shear stress and bending tensile stress are 60 MPa and 140 MPa, respectively. As per IS 800 : 2007 the equivalent stress will be MPa.

1. 174.36

The escape velocity from a planet is $v_0$. The escape velocity from a planet having twice the radius but same density will be

A boy's catapult is made of rubber cord which is $42cm$ long, with $6mm$ diameter of cross-section and of negligible mass. The boy keeps a stone weighing $0.02kg$ on it and stretches the cord by $20cm$ by applying a constant force. When released, the stone flies off with a velocity of $20m{s}^{-1}$. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to

Two identical particles of mass m carry a charge Q each. Initially one is at rest on a smooth horizontal plane and the other is projected along the plane directly towards first particle from a large distance with speed $v_0$. The closed distance of approach be

A uniform rigid rod of mass $m$ and length $l$, is being rotated in a horizontal plane about a vertical axis, passing through one end $A$. If $T_B$ and $T_C$ are the tensions in the rod at points $B$ and $C$, then choose the correct option, if $B$ is the mid point of the rod.

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth $($mass = $5.98\times {10}^{24}\text{kg})$ has to be compressed to be a black hole?

A uniform solid cylinder of mass 'm' can rotate freely about its axis which is kept horizontal. A particle of mass $m_0$ hangs from the end of a light string wound round the cylinder. When the system is allowed to move, the acceleration with which the particle descends is

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If $m$ is mass of the photo-electron emitted from the surface and has de-Broglie wavelength ${\lambda }_d$, then -