A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration 2 m/s2 and the car has acceleration 4 m/s2 . The car will catch up with the bus after a time of :

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

The maximum velocity of the photoelectrons emitted from the surface is v when light of frequency n falls on a metal surface. If the incident frequency is increased to 3n, the maximum velocity of the ejected photoelectrons will be :

A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are : [Take Planck's constant h $$=$$ 6.62 $$\times$$ 10$$-$$34 Js]

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $${\lambda }_A$$ to $${\lambda }_B$$ after the collision is:

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It produces continuous as well as characteristic X-rays. If $$\lambda$$min is the smallest possible wavelength of X-ray in the spectrum, the variation of log$$\lambda$$min with log V is correctly represented in:

A magnetic needle of magnetic moment 6.7 $$\times$$ 10-2 A m2 and moment of inertia 7.5 $$\times$$ 10-6 kg m2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

If the Earth has no rotational motion, the weight of a person on the equator is W. Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh {3 \over 4} W. Radius of the Earth is 6400 km and g=10 m/s2.

The mass density of a spherical body is given by $$\rho$$ (r) = {k \over r} for r $$\le$$ R and $$\rho$$ (r) = 0 for r > R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is :

The variation of acceleration due to gravity $$g$$ with distance d from centre of the earth is best represented by (R = Earth’s radius):

A single slit of width b is illuminated by a coherent monochromatic light of wavelength $$\lambda$$. If the second and fourthminima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 $$\stackrel{\circ }{A}$$ and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is

A capacitance of 2 $$\mu$$F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $$\mu$$F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:

A combination of parallel plate capacitors is maintained at a certain potential difference. When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by 2.4 mm. Find the dielectric constant of the slab.

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains 4 $$\mu$$C charge, its radius will be : [ Take : {1 \over {4\,\pi { \in _0}}} = 9 $$\times$$ 109 N $$-$$ m2/C2 ]

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 ×108 ms–1)

In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1 and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4 s, the difference in radii, $$|$$r1 $$-$$ r2 $$|$$ is best given by :

Two wires W1 and W2 have the same radius r and respective densities $$\rho$$1 and $$\rho$$2 such that ρ2 = 4$$\rho$$1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2 is :