Download Physics

Time : 3.00 hrs.
KENDRIYA VIDYALAYA NTPC SHAKTINAGAR
HALF YEARLY EXAMINATION 2015-2016
SUB – Physics (Theory)
Class – XI
M.M. – 70
General Instructions.
a) All questions are compulsory.
b) There are 30 questions in total . Questions from 1 to 8 carry 1 mark each , questions from 9 to 18 carry
two marks each , questions from 19 to 27 carry three marks each and questions from 28 to 30 carry five
marks each
Q. 1. Write two physical quantities having dimension (ML2T -2).
Q. 2. Under what condition is the scalar product of two non-zero vectors zero ?
Q. 3. A body just starts to move when 15 N forces is applied . If 10 N forces is applied on it . Find force
of friction .
Q. 4. When momentum of a body is doubled , how will its Kinetic-energy changes?
Q. 5. Write equation of rotational motion equivalent to the following equation of linear motion
v2 – u2= 2as
Q. 6. What would happen to an artificial satellite if its orbital velocity is slightly decreased due to some
defect in it ?
Q. 7. Draw distance time graph for a uniform motion .
Q. 8. At what height above the earth’s surface, the value of g is the same as in a mine 80km deep?
Q. 9. The physical quantity Q is given by Q = ( A2 B 3/2 ) /( C4 D 1/2 ).
The percentage error in A, B, C and D are 1%, 2%, 4%, 2% respectively. Find the percentage error in Q.
Q.10.The time period of a simple pendulum depends on it’s length and acceleration due to
gravity.Derive an expressiondimensionally for the same.
Q.11. Calculate the cross product of thefollowing vectors
A =5î + 2Ĵ + Ќ ,
B = î – 4Ĵ + Ќ
Q.12. Two equal forces have their resultant equal to either . What is the inclination between them?
Q.13. State and prove the theorem of parallel axis for moment of inertia.
Q.14. State and prove Work – Energy Theorem for variable force .
Q.15 A man weighs 70 kg.He stands on a weighing machine in a lift ,which is moving (i) upward with a
uniform speed of 10ms-1(ii) downward with a uniform acceleration of 5 ms-2.What would be the reading
on the scalein each case.
Q.16. Show that the kinetic energy of a rigid body rotating with angular velocity ω is given by ½ Iω2?
Q.17. A shell of mass 0.020kg is fired by a gun of mass 100kg. If the muzzle speed of the shell is 80 m s -1 .
What is the recoil speed of the gun?
Q.18. Establish the fact that the first and third laws of motion of Newton are contained in second law?
Q.19. Three bodies, a ring, a solid cylinder and a solid sphere of the same radii roll down on the same
inclined plane without slipping from the same height . They start from rest. Which bodies reach the
ground with maximum velocity? Write with explanation.
Q.20. A man walks on a straight road from his home to market 2.5 km away with a speed of 5 km/hr.
Finding the market closed , he instantly turns and walks back home with a speed of 7.5 km/hr. What is
the (a) magnitude of average velocity (b) average speed of the man over the interval of time (i) 0 – 30
minutes (ii) 0 – 30 minutes (iii) 0 – 40 minutes ?
Q.21. A helicopter of mass 1000 kg rises with a vertical acceleration of 15 m/s2 . The crew and
passengers weigh 300 kg . Find magnitude and direction of the
(i) Force on the floor by the crew and passengers .
(ii) Action of the rotor of the helicopter on the surrounding air.
(iii) Force on the helicopter due to the surrounding air ?
Q.22. A stone is dropped from a height ‘h’. Prove that the energy at any point in its path is conserved.
Q.23. Define instantaneous power. Develop an expression for it as the scalar product of force and
velocity vectors. Of which physical quantity is the unit kilowatt hour ? Define one kilowatt hour. Express
it in joules.
Q. 24. A railway carriage of mass 9000 kg moving with a speed of 36 kmh-1 collides with a stationary
carriage of the same mass. After the collision , the carriage get coupled and moved together . What is
their common speed after collision ? What type of collision is this ?
Q.25. State and prove law of conservation of angular momentum. Write the location of the centre of
mass of a (i) cylinder (ii) cube , each of uniform density.
Q. 26. Derive the following equations for uniformly accelerated motion from velocity- time graph :
(i) v=u+at (ii) s=ut+1/2 at2 (iii) v2=u2+2as
Q.27. Show that the value of ‘g ‘decreases with the height above the earth’s surface. Derive the
concerned expression.
Q. 28. (a) Derive an expression for centripetal acceleration and state its direction.
(b) A stone tied to
the end of a string 80 cm long is whirled in a horizontal circle with a constant speed . If the stone makes
14 revolutions in 25 seconds, what is the magnitude and direction of acceleration of the stone ?
OR
A projectile is fired with a velocity u making an angle with the horizontal . Show that its trajectory is
aparabola . Derive expressions for (i) time for maximum height (ii) maximum height (iii) Horizontal
range.
Q. 29. (a) Determine the maximum speed with which the vehicle can negotiate a level curved track
safely .
(b) A circular race track of radius 300m is banked at an angle of 150. If the coefficient of friction between
the wheels of a race car and road is 0.2 , what is the (i) optimum speed of the race car to avoid wear and
tear on its tyres and (ii) maximum permissible speed to avoid slipping ? [ tan 150 = 0.2679. ]
Q. 30. (a) Define escape velocity . Derive an expression for the escape velocity of a body from the
surface of the earth .
(b) Show the escape velocity of a body from the earth surface is √2 times its velocity in a circular orbit
just above the earth surface.
( c) An elephant and an ant are to be projected out of earth into space . Do we need different velocities
to do so? Write with reason
OR
(a)
State three Kepler’s laws on
planetary motion with figure if necessary.
(b)
Prove Kepler’s law of areal
velocity.
(c) The time period of the satellite of the earth is 5 hours . If the separation between the earth and the
satellite is increased to 4 times the previous value, what will be the new time period of the
satellite?
.