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The acceleration due to gravity at a height 1/10th of the radius of the earth above the earth's surface is 8.2 ms⁻^{1} Its value at a point at the same distance below the surface of the earth is
The volume of a gas will be double of what it is at 0^{o}C (pressure remaining constant) at
The electric potential at any point (x,y,z) in a space is given by: V=4x^{2} volt. The electric field at (1,0,2) m in space is
Magnitude of electric field at the point (1m, 0, 2m) = − 8 V ∕ m
An L.C. circuit contains 10 mH inductor and a 25 μ F capacitor. The resistance of the circuit is negligible. The energy stored in the circuit is completely magnetic at time (in milli seconds) being measured from the instant when the circuit is closed
When R is negigible,
Therefore, t = 1.57, 4.71, 7.85 ... milli sec
The horizontal range of a projectile is R, when the angle of projection is 30^{o}. The value of another angle of projection, for the same range, is
If a ball of 80 kg mass hits an ice cube and temperature of ball is 100^{o}C, how much ice becomes water? Specific heat of ball is 0.2 cal/gram.
Two uncharged identical capacitors A and B, each of capacitance C, and an inductor of inductance L are arranged as shown in the adjacent figure. At t = 0, the switch S_{1} is closed while switch S_{2} remains open. At time t = t_{0}=√LCπ/2, switch S_{2} is closed while switch S_{1} is opened.
Q. The charge on capacitor A after time t_{0} is
A massless metal plate is placed on a horizontal tabletop lubricated with oil. The sheet is a square of side length ℓ = 1.0m and the oil layer has thickness h = 1.0 mm. Initially one edge of the sheet coincides with one edge of the table. The sheet is pulled outwards without rotation with a constant force F = 15 N. If coefficient of viscosity of the oil is η = 0.2 Ns/m^{2}, how long (in second) will it take to pull half of the sheet out of the table?
Write the value of current i_{3} (in mA) in the circuit shown in the figure.
5 × 10^{3} I_{1} = 60
Potential difference across
10 kΩ = 240 – 60 = 180 V
So, I_{3} × 10 × 10^{3} = 180
⇒ I_{3} = 18 mA
I_{2} = I_{3} – I_{1} = 6 mA
A monochromatic light of wavelength 6500Å is used in YDSE. Now both slits are covered by two thin slab of refractive index 3.2 and 2.7 respectively. By doing so central bright fringe shifts to original 7^{th} bright fringe. If both slabs have same thickness then thickness of slab is (in µm).
A hollow sphere (mass m, radius R) is put inside a hollow cone (mass m, radius 3R and semiangle 30°) as shown in the figure. The whole arrangement is rigidly fixed to the ground at the apex of the cone. Both the sphere and the cone are made of the same material (α = 10^{–4} /°C). Considering that major changes in dimensions could happen only due to heating effects, find the increase in potential energy (in Joule) of the system if it's temperature is increased by 100°C.
A rod is clamped at both of its ends and stationary longitudinal waves are produced in it. In first experiment, the rod has a total of 4 nodes with amplitude of each antinode to be 1 mm. In other experiment, the rod has a total of 6 nodes with amplitude of each anti node to be 2mm. The energy of vibrations in the rod in two cases is E_{1} and E_{2} respectively. Write value of E_{1}/E_{2}.
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