Physics

Two circuits are shown in the figure (a) & (b). At a frequency of __________ rad /s the average power dissipated in one cycle will be same in both the circuits.

A radioactive sample has an average life of 30ms and is decaying. A capacitor of capacitance 200 µF is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _______ Ω.

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Å. If the speed of electron is 2.2 * 10? m/s, then the current associated with the electron will be _______ * 10?² mA. [Take π as 22/7]

Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is √(aGM/(7R)) then the value of 'a' is _______. [Given: The two planets are fixed in their position]

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85 * 10?² A/m² and moment of inertia 5 * 10? kg m². If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is _______ mT. [Take π² as 9.85]

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulate by a 7.7 kHz sine wave of 5 V amplitude are (a/10) V and ( b/10 ) V respectively. Then the value of a/b is _______.

A particle of mass 9.1 * 10?³¹ kg travels in a medium with a speed of 10? m/s and a photon of a radiation of linear momentum 10?²? kg m/s travels in vacuum. The wavelength of photon is _______ times the wavelength of the particle.

A stone of mass 20g is projected from a rubber catapult of length 0.1m and area of cross section 10? m² stretched by an amount 0.04 m. The velocity of the projected stone is _______ m/s. (Young's modulus of rubber = 0.5 * 10? N/m²)

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T? is connected to T?. As the current in R = 6Ω attains a maximum value of steady state level, T? is disconnected from T? and immediately connected to T?. Potential drop across r = 3Ω resistor immediately after T? is connected to T? is _______ V. (Round off to the Nearest Integer)

A prism of refractive index n? and another prism of refractive index n? are stuck together (as shown in the figure). n? and n? depend on λ, the wavelength of light, according to the relation:
n? = 1.2 + (10.8 * 10?¹?)/λ² and n? = 1.45 + (1.8 * 10?¹?)/λ²
The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _______ nm.