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A block rests on a rough inclined plane making an angle of ${30}^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10\text{N}$, the mass of the block (in $\text{kg}$) is (take $g=10{\text{m/s}}^2$)

A block of mass $m=1\text{kg}$ slides with velocity $v=6{\text{ms}}^{-1}$ on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about $\text{O}$ and swings as a result of the collision, making angle $\theta$ before momentarily coming to rest. If the rod has mass $M=2\text{kg}$ and length $l=1\text{m}$, the value of $\theta$ is approximately-



$[$Take $g=10{\text{ms}}^{-2}]$

A vertical electric field of magnitude $4\times {10}^5\text{N/C}$ just prevents a water droplet of mass $1\times {10}^{-4}\text{kg}$ from falling. Find the charge on the droplet.

A bullet of mass $20g$ hits a block of $1.98\text{kg}$ suspended from massless string of length $100\text{cm}$ and sticks to it. The bullet flies down at an angle of ${30}^{\circ }$ to the horizontal with a velocity of $200\text{m/s}$. Through what height will the block rise ?

How much should the pressure on a litre of water be changed to compress it by $0.10\%$. Bulk modulus of water $=2.2\times {10}^9{\text{Nm}}^{-2}$

A tapered circular rod of diameter varying from 60 mm tp 40 mm is connected to another circular tapered rod of diameter varying from 40 mm to 70 mm as shown in the figure below. Both bars are of the same material with $E=2\times {10}^5\text{MPa}$. When subjected to a load of 100 kN, the deflection at point A is mm.

1. 1.52

State three important factors showing the need for translating a low frequency signal into a high frequency wave before transmission.

Draw a sketch of a sinusoidal carrier wave along with a modulating signal and show how these are superimposed to obtain the resultant amplitude modulated wave.

For a finite line charge, the net electric field at any point on equatorial line makes an angle of _______ with the axis of line charge.

Three
girls skating on a circular ice ground of radius 200 m start from a
point Pon the edge of the ground and reach
a point Qdiametrically opposite to Pfollowing different paths as shown
in Fig. 4.20. What is the magnitude of the displacement vector for
each? For which girl is this equal to the actual length of the path
skated?

Figure shows a tube structure in which a sound signal is sent from one end and is received at the other end. The semicircular part has a radius of $10.0\text{cm}$. The frequency of the sound source can be varied electronically between $1000\text{Hz}$ and $4000\text{Hz}$. Find the approximate frequency(s) at which a maxima of intensity is detected.



[The speed of sound in air = $340{\text{ms}}^{-1}$]

The displacement, $y$ of a particle on a straight line is given by $y=f(x,t)$, as a function of time. Which of the following functions does not represent wave motion?

A stretched string of length I, fixed at both ends can sustain stationary waves

of wavelength $\lambda$ given by

[UPSEAT 2000; Pb. PET 2004; CPMT 2005]

Find th evalues of $r_p\mu$ annd $g_m$ of a triode operating at plate voltage 200 $V^p$ and grid voltage -6V. The plate characteristics are shown in figure (41-E1).

The equation of motion of a particle started at $t=0$ is given by $x=10\text{sin}(20t+\frac{\pi }{3})$, where $x$ is in $\text{cm}$ and $t$ is in seconds. Find the time when the particle first comes to rest.

A horizontal board of negligible mass supports a mass weighing $20\text{N}$ at a distance of $2\text{m}$ from the point $A$. Calculate the weight which must be placed at point $B$, which is $5\text{m}$ from point $A$, in order to keep the board in rotational equilibrium?

A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416 Hz. If the length is doubled keeping other things same, the string will

Six bullets of mass $5\text{gm}$ are fired from a gun of mass $5\text{kg}$. What is the speed of the gun if the speed of the bullets w.r.t. the ground is $200\text{m/s}$?

An $LCR$ circuit contains of $100\Omega$ resistance and an $AC$ supply of $200\text{V}$ at $300\text{rad/s}$ angular frequency. When only capacitance is taken out from the circuit, the current lags the voltage by ${60}^{\circ }$. If, on the other hand, only the inductor is taken out, the current leads the applied voltage by ${60}^{\circ }$. The current flowing in the original circuit is,

A mass $6\times {10}^{24}\text{kg}$ (= mass of earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is $3\times {10}^8\text{m/s}$ (equal to that of light). What should be the radius of the sphere ?

A car travels 15 km east at a constant speed of 20 km/hr, then continues east for 20 km at a constant speed of 30 km/hr. What can be said about the magnitude of average velocity?