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The potential energy of mass $1\text{kg}$ at a distance $r\text{m}$ from a fixed point $\text{O}$ is given by $V\left(r\right)=\frac{9r^2}{2}\text{J}$. With the particle moving in a circular orbit of radius $1\text{m}$ about the point $\text{O}$ if $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $\text{O}$, then which of the following statements is/are true?

A mass of 0.5 kg is suspended from a wire, then the length of the wire increases by 3 mm then work done is?

In the ideal double-slit experiment , when a glass-plate (refractive index $1.5$) of thickness $t$ is introduced in the path of one of the interfering beams (wave-length $\lambda )$, the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

Two capacitors of capacitance $4\mu \text{F}\text{and}6\mu \text{F}$are charged to potential of $30\text{V}$ and $20\text{V}$ respectively. If both are connected parallel with positive terminal of the second capacitor and negative terminal with positive terminal of the common potential is

Two elastic rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature is - $({\alpha }_1,{\alpha }_2$ = linear expansion coefficient, $A_1,A_2$ = Area of rods, $Y_1,Y_2$ = Young's modulus, $L_1,L_2$ = lengths )

An object of mass $m_1$ collides elastically with another object of mass $m_2$, which is at rest. After the collision, the objects move with equal speeds in opposite directions. The ratio of the masses, $m_2:m_1$ is -

The minimum angle of incline, for an object on it to begin to slide down, is known as

In SHM, the distance of particle from middle point of its path at three consecutive seconds are found to be $x,y$ and $z$. Then time period of SHM is:

If a particle moves with an acceleration then which of the following can remain constant

A) both speed and velocity

B) neither speed nor velocity

C) only the velocity

D) only the speed

Identify the figure which represents the acceleration of a fluid along horizontal direction:

[MP PET 1990, 2001]

1. 766.04

A body is projected with velocity $u$ at an angle $\theta$ with the horizontal. Another body having double mass is also projected with the same velocity but at an angle $90-\theta$. The ratio of their maximum heights is

The flux of magnetic field through a closed conducting loop changes with time according to the equation, $\Phi =a{t}^2+bt+c$. (a)Write the SI units of a,b and c.(b)If the magnitudes of a,b and c are 0.20, 0.40 and 0.60 respectively, find the induced emf at t=2 s.

For the circuit shown in figure, the node voltage $V_2$ is,

If a ball is dropped from the rest, its bounces from the floor. The coefficient of restitution is 0.5 and the speed just before the first bounce is 5ms^-1. The total time taken by the ball to come to rest is

There is an aeroplane taking off at the airport , at say. 800 Km/ h . A dog on the runway is trying to chase the shadow of the Aeroplane. Take the time to be exactly noon so that the shadow falls Vertically below the plane . How fast must you run to keep up with the shadow?

If $E_1,E_2$ and $E_3$ respectively represent the kinetic energies of an electron, an $\alpha$-particle and a proton each having same de-Broglie’s wavelength, then

A block of mass $m$ held touching the upper end of a light spring of force constant $K$ as shown in the figure. Find the maximum potential energy stored in the spring if the block is released suddenly on the spring.

Given $K_1$ = 1500 N/m, $K_2$ = 500 N/m $m_1$ = 2 kg, $m_2$ = 1 kg, Find Work done in slowly pulling down $m_2$ by 8 cm from equilibrium position.

A sphere of solid material of specific gravity $8$ has a concentric spherical cavity and just sinks in water. Then the ratio of the radius of the cavity to the outer radius of the sphere must be

The distance between the plates of a reactangular parallel plate capacitor (PPC) of plate area $3140{\text{mm}}^2$, whose capacitance is equal to that of an isolated metallic sphere of radius $2\text{m}$ will be

A body of mass $5kg$ is moving along the x-axis with a velocity $2m{s}^{-1}$. Another body of mass $10kg$ is moving along the y-axis with a velocity $\sqrt{3}m{s}^{-1}$. They collide at the origin and stick together. The final velocity of the combined mass is

Two identical balls marked 2 and 3, in contact with each other and at rest on a horizontal frictionless table, are hit head-on by another identical ball marked 1 moving initially with a speed 'v' as shown in the figure. If the collision is elastic, what is observed?

Match the informations about mechanical waves given in column-I with that given in column-II

$\begin{array}{cc}\text{Column - I}& \text{Column - II}\\ \text{(Nature of wave)}& \text{(Properties)}\\ \text{(A) Transverse progressive wave}& \text{(P) Amplitude of all particles is same.}\\ \text{(B) Longitudinal progressive wave}& \text{(Q) Phase of all the particles may be same.}\\ \text{(C) Transverse standing wave}& \text{(R) May occur in gases.}\\ \text{(D) Longitudinal standing wave}& \text{(S) KE and PE of a small element may be maximum}\end{array}$

Which of the following option has the correct combination considering column-I and column-II ?



Note that any information in column-I may have more than one matching options in column-II.

The Boolean expression f(x, y, z) in its canonical form for the decoder circuit shown below:

Find the reading of the spring balance if it is assumed to be of negligible mass.

(Take $g=10m/s^2$)

The scale factor for the two drawings is given by

The wattage rating of a light bulb indicates the power dissipated by the bulb if it is connected across $110\text{V}$ DC potential difference. If a $50\text{W}$ and $100\text{W}$ bulb are connected in series to a $110\text{V}$ DC source, how much power will be dissipated in the $50\text{W}$ bulb?

A charged particle is fired at an angle $\theta$ to a uniform magnetic field directed along the $x–$axis. During its motion along a helical path, if the pitch of the helical path is equal to the maximum distance of the particle from the $x–$ axis, then