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A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first 2 s, it rotates through an angle `theta_1` , in the next 2 s, it rotates through an angle `theta_2` . the ratio of `theta_1/theta_2` is

A body is projected vertically upwards with a velocity of 10 m`s^(–1)`. It reaches the maximum height h in time t. In time `t/2`, the height covered is

At ordinary temperature, the molecules of an ideal gas have only translational and rotational kinetic energies. At high temperatures they may also have vibrational energy. As a result of this at higher temperatures (`C_V` = molar heat capacity at constant volume)

The power factor of the circuit as shown in figure is

In a galvanometer 5% of the total current in the circuit passes through it. If the resistance of the galvanometer is G, the shunt resistance S connected to the galvanometer is

A compound microscope has an eye piece of focal length 10 cm and an objective of focal length 4 cm. Calculate the magnification, if an object is kept at a distance of 5 cm from the objective, so that the final image is formed at the least distance of distinct vision 20 cm

In Young's double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double that from the other slit. If `I_m` be the maximum intensity, the resultant intensity when they ineterfere at phase difference `phi` is given by

The rms value of the electric field of the light coming from the sun is 720 N `C^(–1)`. The average total energy density of the electromagnetic wave is

The amount of work done in stretching a spring from a stretched length of 10 cm to a stretched length of 20 cm is

A thin uniform rod of mass m moves translationary with acceleration a due to two antiparallel forces of lever arm l. One force is of magnitude F and acts at one extreme end. The length of the rod is

A polyster fibre rope of diameter 3 cm has a breaking strength of 150 kN. If it is required to have 600 kN breaking strength. What should be the diameter of similar rope

An electromagnetic wave of frequency 3 MHz passes from vacuum into a dielectric medium with permitivity `epsilon_r =4` , then

A coil of resistance 400 `Omega` is placed in magnetic field. If the magnetic flux `phi`(Wb) linked with the coil varies with time t(s) as `phi= 50t^2 + 4` . The current in the coil at t = 2 s is

A resistor R and `2 muF` capacitor in series are connected through a 200 V direct supply. Acros the capacitor is a neon bulb that llights up at 120 V. Find the value of R to make the bulb light up 5 s after the switch has been closed. (Take `log_(10)`2.5 = 0.4)

A body hanging from a spring stretches it by 1 cm at the earth's surface. how much will the same body stretch the spring at a place 16400 km above the earth"s surface (Radius of the earth = 6400 km)

An electric bulb is marked 100 W, 230 V, If the supply voltage drops to 115 V, what is the heat and light energy produced by the bulb in 20 min

Two slits separated by a distance of 1 mm are illuminated with red light of wavelength `6.5×10^(–7)` metre. The interference fringes are observed on a screen placed one metre from the slits. The distance between the thrid dark fringe and fifth fringe on the same side of centre is equal to

A luminous object is placed at a distance of 30 cm from the convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens a convex mirror of radius of curvature 10 cm be placed in order to have an inverted image of the object coincident with it

In an experiment, a magnet with its mangetic moment along the axis of a circular coil and directed towards the coil, is withdrawn away from the coil and parallel to itself. The current in the coil, as seen by the withdrawing magnet, is

The steady state current in a `2Omega` resistor when the internal resistance of the battery is negligible and the capacitance of the condenser is 0.1 `muF` is

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