Physics (25) Full length

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Q 1.
A particle of mass m with an initial velocity \(u\hat{i}\) collides perfectly elastically with a mass 3 m at rest. It moves with a velocity \(v\hat{j}\)after collision, then, v is given by

Q 2.
Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are \(0.1\;kg-m^2\) and \(10\;rad\;s^{-1}\) respectively while those for the second one are \(0.2\;kg-m^2\) and \(5\;rad\;s^{-1}\) respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The kinetic energy of the combined system is :

Q 3.

The magnetic field of a plane electromagnetic wave is \(\overrightarrow B=3\times10^{-8}sin[200\pi(y+ct)\hat i\;T]\) where \(c=3\times10^8 \;ms^{-1}\)

is the speed of light the corresponding electric filed is :

Q 4.
A small bar magnet is placed with its axis at 30° with an external magnetic field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is:

Q 5.
A body is moving in a low circular or it about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is :

Q 6.
Two identical strings \(X\) and \(Z\) made of same material have tension \(T_x\) and \(T_z\) in then If their fundamental frequencies are \(450Hz\) and \(300Hz\), respectively, then the ratio \(T_x/T_z\) is :

Q 7.
When the temperature of metal wire is increased from 0ºC to 10ºC, its length increases by 0.02%.The percentage change in its mass density will be closed to :

Q 8.
Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

Q 9.
On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by \({A_X\over(x^2+a^2)^{3/2}}\)in the x-direction. The magnitude of the gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity is:

Q 10.

In a photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased :

Q 11.

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is \(\omega\)rad \(s^{-1}\). The difference in the height, h (in cm) of liquid at the centre of vessel and at the will be :

Q 12.
A capillary tube made of glass of radius 0.15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = \(0.05\;Nm^{-1}\) , density = \(667\;kg\;m^{-3}\) ) which rises to height h in the tube. It is observed that the two tangents drawn from observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60º with one another. Then h is close to (g = \(10\;ms^{-3}\) )

Q 13.
A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius \(R_e\). By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it becomes \(\sqrt{3\over2}\) times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :

Q 14.
Two charged thin infinite plane sheets of uniform charge density \(\sigma_+\) and \(\sigma_-\), where \(|\sigma_+|>|\sigma_-|\), intersect at the right angle. Which of the following best represents the electric field lines for the system:

Q 15.
A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force \(mkv^2\) where v is it speed. The maximum height attained by the ball is :

Q 16.
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the \(7^{th}\) division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and \(4^{th}\) VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)

Q 17.

The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\;T\) in it and a proton entering the region with velocity \(4\times10^5\;ms^{-1}\) making an angle \(60^\circ\) with the field. If the proton completes 10 revolution by the time it cross the region shown, \('l'\) is close to (mass of proton = \(1.67\times10^{-27}\;kg\) , charge of the proton = \(1.6\times10^{-19}\;C\))

Q 18.
In a radioactive material, fraction of active material remaining after tie t is \(\frac9{16}\) . The fraction that was remaining after t/2 is :

Q 19.
A beam of plane polarised light of large cross-sectional area and uniform intensity of \(3.3\;Wm^{-2}\) falls normally on a polariser(cross sectional area \(3\times10^{-4}\;m^2\) ) which rotates about its axis with an angular speed of \(31.4\) rad/s. The energy of light passing through the polariser per revolution, is close to:

Q 20.
A capacitor \(C\) is fully charged with voltage \(V_0\). After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance \(C/2\). The energy loss in the process after the charge is distributed between the two capacitors is :

Q 21.
A 5\(5_\mu F\) capacitor is charged fully by a \(220\;V\)supply. It is then disconnected from the supply and is connected in series to another uncharged \(2.5_\mu F\) capacitor. If the energy change during the charge redistribution is \(\frac {X} {100} \;J\) then value of \(X\)to the nearest integer is :
Q 22.

A particle of mass m is moving along the x-axis with initial velocity \(u\hat i\) . It collides elastically with a particle of mass \(10m\) at rest and then moves with half its initial kinetic energy (see figure). If \(sin\theta_1=\sqrt{n}\sin\theta_2\) then value of n is ________.

Q 23.
A Bakelite beaker has volume capacity of \(500\;cc\) at \(30^\circ C\). When it is partially filled with \(V_m\) volume (at \(30^\circ C\)) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{(beaker)}=6\times10^{-6} \ C^{-1}\) , where \(\gamma\)is the coefficient of volume expansion, then \(V_m(in\;cc)\) is close to ………….
Q 24.

ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid-points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about a axis passing through G and perpendicular to the plane ABC is \(I_0\). If part ADE is removed, the moment of inertia of the remaining part about the same axis is \(NI_0\over16\) where N is an integer. Value of N is :

Q 25.

Four resistance \(40\Omega,60\Omega,90\Omega,\;and\;110\Omega\) make the arms of a quadrilateral ABCD. Across AC is a battery of emf \(40V\) and internal resistance negligible. The potential difference across BD in V is ……

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