Class XI
Annual Exam - 2018-19
(solved Paper)
Section 'C'
13. A particle starts from origin at t=0 with a velocity 5.0 i m/s and moves in x-y plane under action of a force which produces a constant acceleration of (3.0i + 2.0j) m/s2.
a) what is the y coordinate of the particle at the instant if its x coordinate is 84m?
b) What is the speed of the particle at this time?
Solution:
b) What is the speed of the particle at this time?
Solution:
14. consider a simple pendulum, having a bob attached to a string, that
oscillates under the action of the force of gravity. Suppose that the period of oscillation of the
simple pendulum depends on its length(l), mass of the bob(m) and acceleration
due to gravity(g).Derive the expression for its time period using method of
dimensions.
Solution: The time period depends on length of the string l, the mass of the bob m and the acceleration due to gravity g and its dependence can be shown as
15. State Work Energy Theorem. Prove it for a variable force.
Solution: Work Energy Theorem
This
theorem states that the work done by the net force acting on a body is equal to
the change produced in the kinetic energy of the body.
16. A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.5 × 108 km away from the sun?
Solution: Let time period of
Saturn be T’ and time period of the earth be T. The distance
of the Saturn from the earth be a’ and the distance of the earth from the sun be a.
17. Find out the position of center of mass of two particle system.
Solution:
Center of mass (COM) of a body is defined as a point at which the entire mass of the body or a system of bodies is supposed to be concentrated.
Center of mass (COM) of a body is defined as a point at which the entire mass of the body or a system of bodies is supposed to be concentrated.
18. State Kepler's laws of planetary motion.
Solution :
Kepler's laws of Planetary motion
OR
Define orbital velocity of a nearest satellite revolving around the earth and obtain its expression.
Solution :
Orbital velocity of a satellite revolving around the earth can be defined as the minimum velocity with which a satellite revolves around the earth.
20. Derive an expression for the work done in an isothermal process.
Solution:
23. A transverse harmonic wave on a string is described by y(x,t) = 3.0sin(36t + 0.018x + π/4), where x and y are in cm and t is in sec. the positive direction of x is from left to right.
a) is this a travelling wave or a stationery wave?
b) what are its amplitude and frequency?
Solution:
a) y(x,t) = 3.0sin(36t + 0.018x + π/4) ...............(i)
the equation of a travelling wave is given by,
y(x,t) = Asin(wt + 0.018x + Φ) ...............(ii)
compairing equations (i) and (ii) we find that the given equation is in the form of travelling wave.
b) compairing equations (i) and (ii) we get,
Amplitude = 3.0m
thus the frequency of the wave is 5.73 Hz
24. Derive an expression for the time period of the horizontal oscillation of a massless loaded spring.
Solution :
Kepler's laws of Planetary motion
Define orbital velocity of a nearest satellite revolving around the earth and obtain its expression.
Solution :
Orbital velocity of a satellite revolving around the earth can be defined as the minimum velocity with which a satellite revolves around the earth.
19. Obtain following equations from first principles:
i) w = w0 + at
ii) q = w0t+ 1/2 at2
Solution: The above equations of motion are derived as below:
i) here, w is the final velocity, w0 is the initial velocity, a is the acceleration, q is the displacement and t is the time taken.
20. Derive an expression for the work done in an isothermal process.
Solution:
A
Process in which there is a change in the pressure and the volume of a gas, but
the temperature remains constant. There is a free exchange of heat between the
gas and surroundings. e.g. boiling process and melting process are isothermal
process.
In
an isothermal process temperature remains constant thus,
PV = Constant
21 . State law of equipartition of energy. Using this law, determine the values of CP, CV and Y for diatomic gases.
Solution:
According to law of equipartition of energy,
the total energy is distributed equally amongst all the degrees of freedom of a
system and the energy associated with each molecule per degree of freedom is 1/2 KBT.
22. Derive Newton's formula for speed of sound in an ideal gas. what is Laplace Correction?
Solution :
Newton's Formula for velocity of sound in an ideal gas:
Sound travels through a
gas in the form of compressions and rarefactions. Newton assumed that the
changes in pressure and volume of a gas, when sound waves are propagated
through it are isothermal.
Laplace Correction for velocity of sound in gases
The result obtained as the speed of sound in STP is 280
which
is different from the experimental value of 331
. This mistake was pointed out by Laplace.
According to Laplace, the changes in pressure and volume of a gas, when
sound waves are propagated through it are not isothermal but are adiabatic.
This value agrees fairly well with the
experimental value of the velocity of sound in air. Thus, the above relation is
the correct relation for the velocity of sound in air.
23. A transverse harmonic wave on a string is described by y(x,t) = 3.0sin(36t + 0.018x + π/4), where x and y are in cm and t is in sec. the positive direction of x is from left to right.
a) is this a travelling wave or a stationery wave?
b) what are its amplitude and frequency?
Solution:
a) y(x,t) = 3.0sin(36t + 0.018x + π/4) ...............(i)
the equation of a travelling wave is given by,
y(x,t) = Asin(wt + 0.018x + Φ) ...............(ii)
compairing equations (i) and (ii) we find that the given equation is in the form of travelling wave.
b) compairing equations (i) and (ii) we get,
Amplitude = 3.0m
24. Derive an expression for the time period of the horizontal oscillation of a massless loaded spring.
Solution :
){kind=link}
0 Comments