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The distance of the closest approach of an alpha particle fired at nucleus with momentum $P$ is $r_0$. The distance of the closest approach when the alpha particle is fired at the same nucleus with momentum $2P$ will be

An electromagnetic wave going through vacuum is described by E = $E_{o}sin(kx-\omega t);B=B_{o}sin(kx-\omega t);$. Which of the following equation is true

A particle is aimed at a mark which is in the same horizontal plane as that of point of projection. If it falls $10m$ short of the target when it is projected with in elevation of ${75}^o$ and fall $10m$ ahead of the target when it is projected with an elevation of ${45}^o$. 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)

A stone is projected from the point on the ground in such a direction so as to hit a bird on the top of a telegraph post of height $h$ and then attain the maximum height $\frac{3h}{2}$ above the ground. If at the instant of projection, the bird were to fly away horizontally with uniform speed, find the ratio between horizontal velocities of the bird and stone if the stone still hits the bird while descending.

A projectile of mass 50 kg is projected vertically upward with a velocity of 100 m/s. After 5 seconds it explodes into two pieces, one piece of 20 kg moving vertically upward with a velocity of 150 m/s. The algebraic sum of the momentum of the system 3 seconds later is

A smooth block of mass $10\text{kg}$ is released from rest from a height $5\text{m}$. It slides and compresses the spring of stiffness as shown in figure $200\frac{\text{N}}{\text{m}}.$ The maximum compression of the spring is

A shell of mass '2m' fired with a speed 'u' at an angle $\theta$ to the horizontal explodes at the highest point of its motion into two fragments of mass 'm' each. If one fragment, falls vertically, the distance at which the other fragment falls from the gun is given by

In a meter bridge, the gaps are closed by resistance $2\Omega$ and $3\Omega$. The value of shunt to be added to $3\Omega$ resistor to shift the balancing point by $22.5\text{cm}$ is

Which of the following is a necessary and sufficient condition for S.H.M.

[NCERT 1974]

A magnetic field of $2\times {10}^{-2}T$ acts at right angles to a coil of area $100c{m}^2$, with $50$ turns. The average e.m.f. induced in the coil is $0.1V$, when it is removed from the field in $t$ $sec$. The value of $t$ is

Figure (15-E11) shows a string stretched by a block going over a pulleys. The string vibrates in its tenth harmonic in unison with a particular tuning fork. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the desnity of the material of the block.

A non-conducting spherical shell of radius R and uniformly charged on its surface with charge 2Q, is rotating about its diametrical axis with a constant angular velocity $\frac{\omega }{2}$. The magnetic dipole moment of the spherical shell is



R त्रिज्या के एक अचालक गोलीय कोश के पृष्ठ को आवेश 2Q द्वारा एकसमान रूप से आवेशित किया जाता है, यह नियत कोणीय वेग $\frac{\omega }{2}$से अपने व्यासतः अक्ष के सापेक्ष घूर्णन कर रहा है। गोलीय कोश का चुम्बकीय द्विध्रुव आघूर्ण है

Is displacement-time graph different from position time graph? How? Explain with an example

A
galvanometer coil has a resistance of 15 Ω and
the metre shows full scale deflection for a current of 4 mA. How will
you convert the metre into an ammeter of range 0 to 6 A?

A moving coil galvanometer of $50\Omega$ resistance gives full deflection when a current of $0.5\text{mA}.$ To convert this galvanometer into a voltmeter of $10\text{V}$ range, the resistance to be connected in series with the galvanometer is

A solenoid has $1000$ turns and $20\text{cm}$ long. Find the magnetic induction produced at the centre of the solenoid by the current of $2\text{A}$.

Which Gaussian surface would you prefer to choose if you had to calculate electric field due to a charge distribution such that the integration complexity is reduced?

The angular displacement of a particle is given by $\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$, where ${\omega }_0$ and $\alpha$ are constant and ${\omega }_0=1\text{rad/sec},\alpha =1.5{\text{rad/sec}}^2$. The angular velocity $($in $\text{rad/s})$ at time, $t=2\text{sec}$ will be

A projectile is thrown from the ground with an initial velocity of $(4\hat{i}+3\hat{j})$$m/s$. It reaches its greatest height above the ground after (Take $g=10m/s^2$)

Four point masses each of mass ${}^{\prime }{m}^{\prime }$ are placed at four vertices $\text{A, B, C}$ and $\text{D}$ of a regular hexagon of side ${}^{\prime }{a}^{\prime }$ as shown in figure. Find the gravitational field strength at the centre $\text{O}$ of the hexagon.

White light is used to illuminate the two slits in YDSE. The separation between the slits is b and the screen is at a distance d (>>b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

Force constant of a spring is $100\text{N/m}$. If both the blocks of mass $10\text{kg}$ and $12\text{kg}$ attached with spring and string are at rest. Then find the extension in spring. Take $g=10{\text{m/s}}^2$.

A particle of mass $m$ is projected at time $t=0$ from a point $P$ on the ground with a speed $v_0$, at an angle of ${45}^{\circ }$ to the horizontal. What is the magnitude of the angular momentum of the particle about $P$ at time $t=\frac{v_0}{g}$?

Which of the following examples represent periodic motion?

(a) A swimmer completing one (return) trip from one bank of a river to the other and back.

(b) A freely suspended bar magnet displaced from its N-S direction and released.

(c) A hydrogen molecule rotating about its center of mass.

(d) An arrow released from a bow.

The ratio of the adiabatic to isothermal elasticities of a triatomic gas is

A nucleus with mass number $220$ initially at rest emits an $\alpha -$particle. If the $Q$ value of the reaction is $5.5\text{MeV}$ then the kinetic energy $\left(\text{in MeV}\right)$ of the $\alpha -$particle is