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Suppose an electron is attracted towards the origin by a force k/r where 'k' is a constant and 'r' is the distance of the electron from the origin . By applying Bohr model to this system , the radius of the n^{th} orbital of the electron is found to be 'r'_{n} and the kinetic energy of the electron to be T_{n} . Then which of the following is true ?
If 3.8 x 10^{6} is added to 4.2 x 10^{5} giving due regard to significant figures, then the result will be
A parallel plate capacitor is first charged and then a dielectric slab is introduced between the plates after disconnecting it from the battery. The quantity that remains unchanged is
When two deuterium nuclei fuse together, in addition to tritium, we get a
If two bodies are projected at 30^{o} and 60^{o} respectively, with the same velocity, then
The wavelength of ultrasonic waves in air is of the order of
70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30^{o}C to 35^{o}C. The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is nearly (Gas constant = 1.99 cal/Kmole)
A boy of mass 42 Kg eats bananas of 980 calories. If this energy is used up to lift him from the ground, the height to which he can move up is
Height = h.
Potential Energy (P.E) = 980 Calories = 4100.32 Jule
Now P.E = mgh
4100.32 = 42 x 9.8 x h
h = 4100.32/42x9.8 ≈ 10m
In the given circuit the capacitor (C) may be charged through resistance R by battery V by closing switch S_{1}. Also when S_{1} is opened and S_{2} is closed the capacitor is connected in series with inductor (L).
Q. At the start, the capacitor was uncharged. When switch S_{1} is closed and S_{2} is kept open, the time constant of this circuit is τ. Which of the following is correct?
A plastic circular disc of radius 10 cm is placed on a thin oil film of thickness 2 mm, spread over a flat horizontal surface. The torque (Nm) required to spin the disc about its central vertical axis with a constant angular velocity 8 rad/sec is (coefficient of viscosity of oil is 1.0 kg/ms) (take π = 3.14)
Calculate the value of output voltage V_{0} (in V) if the Si diode and Ge diode conduct at 0.7 V and 0.3V respectively as shown in figure.
In Young's double slit experiment, the wavelength of red light is 7800 Å and that of blue light is 5200 Å. The minimum value of n for which n^{th} bright band due to red light coincides with (n + 1)^{th} bright band due to blue light, is :
n (7800) = (n + 1) 5200
A railway track (made of iron) is laid in winter when the average temperature is 18°C. The track consists of sections of 12.0 m placed on after the other. How much gap (in cm) should be left between two such sections so that there is no compression during summer when the maximum temperature goes to 48°C ? Coefficient of linear expansion of iron = 11 × 10^{–6}/°C.
ΔL = L_{0} α ΔT
= 12 × 11 × 10^{–6} × 30
= 3960 × 10^{–6} m
A string of mass per unit length μ is clamped at both ends such that one end of the string is at x = 0 and the other end at x = L. When string vibrates in fundamental mode, amplitude of the midpoint of string is a and tension in string is F. Find the total oscillation energy (in J) stored in the string. (Use L = 1m, F = 10 N, a = 1/πm)
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