HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Important Questions

The number of degrees of freedom for a rigid diatomic molecule is.................

(a) 3

(b) 5

(c) 6

(d) 7

Two particles perform linear simple harmonic motion along the same path of length 2A and period T as shown in the graph below. The phase difference between them is ___________.

Calculate the kinetic energy of 10 gram of Argon molecules at 127°C.
[Universal gas constant R = 8320 J/k mole K. Atomic weight of Argon = 40]

A copper metal cube has each side of length 1 m. The bottom edge of the cube is fixed and tangential force 4.2x10⁸ N is applied to a top surface. Calculate the lateral displacement of the top surface if modulus of rigidity of copper is 14x10¹⁰ N/m².

State an expression for K. E. (kinetic energy) and P. E. (potential energy) at displacement ‘x’ for a particle performing linear S.H. M. Represent them graphically. Find the displacement at which K. E. is equal to P. E.

When the length of a simple pendulum is decreased by 20 cm, the period changes by 10%. Find the original length of the pendulum.

The phase difference between displacement and acceleration of a particle performing S.H.M. is _______.

(A) `pi/2rad`

(B) π rad

(C) 2π rad

(D)`(3pi)/2rad`

In a damped harmonic oscillator, periodic oscillations have _______ amplitude.

(A) gradually increasing

(B) suddenly increasing

(C) suddenly decreasing

(D) gradually decreasing

Prove the law of conservation of energy for a particle performing simple harmonic motion.Hence graphically show the variation of kinetic energy and potential energy w. r. t. instantaneous displacement.

Assuming the expression for displacement of a particle starting from extreme position, explain graphically the variation of velocity and acceleration w.r.t. time.

A clock regulated by seconds pendulum, keeps correct time. During summer, length of pendulum increases to 1.005 m. How much will the clock gain or loose in one day?

(g = 9.8 m/s² and π = 3.142)

A particle executes S.H.M. with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy.

Define practical simple pendulum

Answer in brief:

Derive an expression for the period of motion of a simple pendulum. On which factors does it depend?

The kinetic energy of nitrogen per unit mass at 300 K is 2.5 × 106 J/kg. Find the kinetic energy of 4 kg oxygen at 600 K. (Molecular weight of nitrogen = 28, Molecular weight of oxygen = 32)

A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:

a) Angular frequency

b) frequency of vibration.

A particle executing linear S.H.M. has velocities v₁ and v2 at distances x₁ and x₂ respectively from the mean position. The angular velocity of the particle is _______

Show that motion of bob of the pendulum with small amplitude is linear S.H.M. Hence obtain an expression for its period. What are the factors on which its period depends?

Show variation of displacement, velocity, and acceleration with phase for a particle performing linear S.H.M. graphically, when it starts from the extreme position.

Show that, under certain conditions, simple pendulum performs the linear simple harmonic motion.