HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

A particle performing linear S.H.M. of period 2π seconds about the mean position O is observed to have a speed of `"b" sqrt3` m/s, when at a distance b (metre) from O. If the particle is moving away from O at that instant, find the time required by the particle, to travel a further distance b.

The displacement of an oscillating particle is given by x = a sin ω t + b cos ω t where a, b and ω are constants. Prove that the particle performs a linear S.H.M. with amplitude A = `sqrt("a"^2 + "b"^2)`.

A wooden block of mass m is kept on a piston that can perform vertical vibrations of adjustable frequency and amplitude. During vibrations, we don’t want the block to leave the contact with the piston. How much maximum frequency is possible if the amplitude of vibrations is restricted to 25 cm? In this case, how much is the energy per unit mass of the block? (g ≈ π² ≈ 10 m/s^-2)

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When an air column in a pipe closed at one end vibrates such that three nodes are formed in it, the frequency of its vibrations is  _____ times the fundamental frequency.

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If two open organ pipes of length 50 cm and 51 cm sounded together produce 7 beats per second, the speed of sound is ______.

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The tension in a piano wire is increased by 25%. Its frequency becomes ______ times the original frequency.

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A string is fixed at the two ends and is vibrating in its fundamental mode. It is known that the two ends will be at rest. Apart from these, is there any position on the string which can be touched so as not to disturb the motion of the string? What will be the answer to this question if the string is vibrating in its first and second overtones? 

A photocell is used to automatically switch on the street lights in the evening when the sunlight is low in intensity. Thus it has to work with visible light. The material of the cathode of the photocell is ______.

If N_Red and N_Blue are the numbers of photons emitted by the respective sources of equal power and equal dimensions in unit time, then ______.

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The equation E = pc is valid ______.

A sonometer wire of length 0.5 m is stretched by a weight of 5 kg. The fundamental frequency of vibration is 100 Hz. Calculate the linear density of wire.

The optical path of a ray of light of a given wavelength travelling a distance of 3 cm in flint glass having refractive index 1.6 is the same as that on travelling a distance x cm through a medium having a refractive index 1.25. Determine the value of x. 

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In a double-slit arrangement, the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits.

1. What is the angular separation in radians between the central maximum and an adjacent maximum?
2. What is the distance between these maxima on a screen 50.0 cm from the slits?

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The distance between two consecutive bright fringes in a biprism experiment using the light of wavelength 6000 Å is 0.32 mm by how much will the distance change if light of wavelength 4800 Å is used?

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A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation on charge, potential, capacitance respectively are ______.

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If the difference between the radii of the two spheres of a spherical capacitor is increased, state whether the capacitance will increase or decrease.

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A spherical shell of radius b with charge Q is expanded to a radius a. Find the work done by the electrical forces in the process.

In Young’s double-slit experiment, the two coherent sources have different intensities. If the ratio of the maximum intensity to the minimum intensity in the interference pattern produced is 25:1, what is the ratio of the intensities of the two sources?

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In Young's double-slit experiment, a thin uniform sheet of glass is kept in front of the two slits, parallel to the screen having the slits. The resulting interference pattern will satisfy:

White light consists of wavelengths from 400 nm to 700 nm. What will be the wavelength range seen when white light is passed through a glass of refractive index 1.55?