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1. 6.604

When two tuning forks A and B are sounded together, 4 beats per second are heard. The frequency of the fork B is 384 Hz. When one of the prongs of the fork A is filed and sounded with B, the beat frequency increases, then the frequency of the fork A is

Answer the following questions:

(a) Time period of a particle in SHM depends on the force constant
k and mass m of the particle:

.
A simple pendulum executes SHM approximately. Why then is the time
period of a pendulum independent of the mass of the pendulum?

(b) The motion of a simple pendulum is approximately simple
harmonic for small angle oscillations. For larger angles of
oscillation, a more involved analysis shows that T is greater
than.
Think of a qualitative argument to appreciate this result.

(c) A man with a wristwatch on his hand falls from the top of a
tower. Does the watch give correct time during the free fall?

(d) What is the frequency of oscillation of a simple pendulum
mounted in a cabinthat is freely falling under gravity?

A stone is thrown vertically upwards with an initial velocity of $30\text{m/s}$. The time taken for the stone to rise to its maximum height is

[Take $g=10{\text{m/s}}^2$]

The figure shows a meter bridge circuit with $\text{AB}=100\text{cm},X=12\Omega$ and $R=18\Omega$, and the jockey $J$ is at the balance point. If $R$ is now made $8\Omega$, through what distance will $J$ have to be moved to obtain a balanced bridge ?

If a body of mass 'm' is moving on a rough
horizontal surface of coefficient of kinetic friction, μ, the net
electromagnetic force exerted by surface on the body is

If the speed of a car is given as $v=2t+2\text{m/s}$, the average speed in $10sec$ is

A wire $\text{PQ}$ of mass $10\text{g}$ is at rest on two parallel metal rails. The separation between the rails is $4.9\text{cm}$. A magnetic field of $0.80$ tesla is applied perpendicular to the plane of the rails, directed inwards. The resistance of the circuit is slowly decreased. When the resistance decreases to below $200\Omega$, the wire $\text{PQ}$ begins to slide on the rails. The coefficient of friction between the wire and the rails is

1. 10

A car starts with $10\frac{m}{s}$ and accelerates with constant acceleration of $5\frac{m}{s^2}$. Find the final speed achieved by the car after $10$ sec.

Twelve resistors each of resistance $r$ are connected together so that each lies along the edge of the cube as shown in the figure. The equivalent resistance between points $1$ and $3$ is

A block is placed on a rough floor and a horizontal external force F is applied on it. The force of friction f by the floor on the block is measured for different values of F and a graph is plotted between them. (taking f on Y and F on X axis)

A hydrogen atom moving at a speed v absorbs a photon of wavelength 122 nm and stops. Find the value of v. Mass of a hydrogen atom $=1.67\times {10}^{-27}$ kg.

Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.14, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.50 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?

A particle is taken to a height $R$ above the earth's surface, where $R$ is the radius of earth. The acceleration due to gravity there is

In the circuit shown below, the ammeter and the voltmeter readings are 3 A and 6 V respectively. Then the value of the resistance R is

A cantilever beam of $l$ subjected to a uniformly distributed load ${}^{\prime }{w}^{\prime }$ per unit length resting on a rigid prop at the tip of cantilever. The magnitude of the reaction at the prop is:

A bead 'B' of mass m is attached to one end of a spring(AB) of natural length R and spring constant K= ($\sqrt{3}$+1)mg/R. The normal reaction at B just after it is released to move is:

Two point masses $m$ and $4m$ are separated by a distance $d$ on a straight line as shown in figure. A third point mass $m_o$ is to be placed at a point on the line such that the net gravitational force on it is zero.





The distance of the $m_0$ from the $m$ is

Can an electromagnetic wave exert force on a proton or an electron ? I think it should. It is because light has both electric and magnetic components . What is your opinion?

Two particles A & B are projected with same speed so that the ratio of their maximum height reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of their horizontal ranges is

One quarter sector is cut from a uniform disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centerof the original disc. Its moment of inertia about the axis of rotation is

In a NPN transistor, 108 electrons enter the emitter in ${10}^{-8}\text{sec.}$ If $1\%$ electrons are lost in the base, the fraction of current that enters the collector and current amplification factor are respectively

A transverse wave is described by the equation $Y=Y_0\sin 2\pi (ft-\frac{x}{\lambda })$. The maximum particle velocity is equal to four times the wave velocity, if

Loop $\text{A}$ of radius $r(<<R)$ moves towards loop $\text{B}$ with a constant velocity $v$ in such a way that their planes are always parallel. What is the distance between the two loops $\left(x\right)$ when the induced e.m.f in loop $\text{A}$ is maximum?

In a medium in which a transverse progressive wave is travelling, the phase difference between two points with a separation of 1.25 cm is $\left(\frac{\pi }{4}\right)$. If the frequency of wave is 1000 Hz its velocity will be

The fraction of a floating object of volume $V_0$ and density $d_0$ above the surface of a liquid of density d will be

The ends of a rod of length $2\text{m}$ and mass $1\text{kg}$ are attached to two identical springs $(k=200\text{N/m})$, as shown in figure.





The rod is free to rotate about its centre $\text{C}$ The rod is depressed slightly at end $\text{A}$ and release. What is the time period of oscillation.

In a gravity free room a man of mass $m_1$ is standing at a height $h$ above the floor. He throws a ball of mass $m_2$ vertically downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the ground.

(Neglect the height of the man)