Subject: Physics
Class XI
Time Allowed: 3 hours
Max. Marks: 70
SECTION – A
1. Is it possible for a body to be accelerated, if its speed is constant? If it is so, give an example.
2. A body of mass m moves along X-axis such that its position co-ordinate at any instant t is x =at4 –bt3 + ct, where a, b and c are constants. What is the force acting on the particle at any instant t?
3. A bullet weighing 10 g is fired with a velocity of 800 m/s. After passing through a mud wall 1 m thick, its velocity decreases to 100 m/s. Find the average resistance offered by the mud wall.
4. A body constrained to move in the Y-direction, is subject to a force, F = this force (-2i+ 15j+6k) N. What is the work done by in moving the body through a distance of 10 m along the Y-axis?
5. Find the value of m so that the vector 3i – 2j + k is perpendicular to the vector 2i + 6j + mk
SECTION – B
6. The acceleration time graph for a body is shown below Fig. Plot the graph. Also plot the corresponding velocity(v)- time(t) corresponding displacement (S) against time(t).
7. Find the dimensions of (a/b) in the equation: P = (a – t2)/bx, where P is pressure, x is distance and t is time.
8. A particle starts from the origin at t= 0 with a velocity of 8.0 j m/s and moves in the xy plane with a constant of (4.0 i +2.0 j) m/s? At the instant the particle’s x coordinate is 29 m, what are (a) its y-coordinate and (b) its speed?
9. Find a vector whose length is 7 and which is perpendicular to each of the vectors. A =2i – 3j + 6k and B = i + i – k
10. If A and B are two such vectors that |A| =2, |B| = 7, and A x B = 3i + 2j + 6k, find the angle between A and B.
11. A batsman hits back a ball straight in the direction of the bowler without changing its initial mass of speed of 12 ms-1. If the ball is 0.15 kg, determine the impulse imparted to the ball. (Assume linear motion of the ball).
12. Derive expression for displacement in t time by graphical method.
SECTION – C
13. Derive Planck’s length in terms of G, c and h, where G is gravitation constant, c velocity of light and h is plank constant.
14. A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. For sliding the block, A on B, a horizontal force of 12 N is required to be applied on B so that both A and B move together? Also find out the acceleration produced by this force.
15. An elevator and its load weigh a total of 800 kg. find the tension T in the supporting cable when the elevator, originally moving downwards at 20 ms-1 is brought to rest with constant retardation in a distance of 50 m.
16. A car starting from rest has a speed of 30 km/h at any one instant. Two seconds later, its speed is 36 km/h and 2 seconds after that, it is 42 km/h.
(i) What is its acceleration in m/s2?
(ii) If it continues to accelerate like this, what will its speed be at 8 seconds, at 9 second after instant?
(iii) What was its speed 4 seconds before its speed was 30 km/h?
17. Determine the angles which the vector A = 5i + 0j + 5k makes with X-axes.
18. In an experiment, the following observations were recorded: L = 2.820 m, M = 3.00 kg, l= 0.087cm, Diameter D = 0.041 cm. Taking g= 9.81 m/s2 using the formula, Y= 4Mg/πD2l. Find the maximum permissible error in Y.
19. A body is projected such that is kinetic energy at the top is % of its initial kinetic energy. What is the initial angle of projection of the projectile with the horizontal?
20. A ball is thrown from the top of a tower with an initial velocity of 10 m/s at an angle of 30° with the horizontal. If it hits the ground at a distance of 17.3 m from the base of the tower, calculate the height of the tower.
21. A body of weight 200 N is suspended with the help of strings as shown in Fig. Find the tensions T1 and T2
22. Two billiard balls each of mass 0.05 kg moving in opposite directions with speed of 6 m/s collide and rebound with the same speed. What is the impulse imparted to each ball by the other?
23. Three identical blocks, each having a mass m are pushed by a force F on a frictionless table as shown in Fig. What is the acceleration of the blocks? What is the net force on the block A? What force does A apply on B? What force does B apply on C? Show action-reaction pairs on the contact surfaces of the blocks.
24
i. The relation between time t and distance x is t = α x2 + β x, where α and β are constants. The retardation is (v is the velocity)
a) 2 αv3 b) 2 βv3 c) 2 αβv3 d) 2 β2v3
ii. A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 sec on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is
a) 3 m/s2 b) -3 m/s2 c) 0.3 m/s2 d) – 0.3 m/s2
iii. The graph of displacement v/s time is
iv. Its corresponding velocity-time graph will be
SECTION D
25. (a) The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms-2. At what distance from the starting point does the box fall off the truck? Ignore the mass of the box.
(b) The initial speed of a body of mass 2.0 kg is 5.0 ms-1. A force acts for 4 s in the direction of motion of the body. The force- time graph is shown in Fig. Calculate the impulse of the force and the final speed of the body.
26. What do you mean by a projectile. Derive expressions for maximum height, time of flight and horizontal range. Show that the path of a projectile is parabolic.
27. (a) CASE STUDY BASES QUESTIONS:
An auto-mobile and a truck starts from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.1 m/s2 and the automobile has acceleration 3.4 m/s2. The auto-mobile overtakes the truck after the truck has moved 40 m.
i. How far was the automobile behind the truck initially?
(A) 24.8 m (B) 30 m (C) 50 m (D) 60 m
ii. The distance moved by automobile before it overtakes the truck-
(A) 54.8 m (B) 64.8 m (C) 74.8 m (D) 68.8 m
27. (b) Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any loss of speed, as shown in Fig. What is (i) the direction of the force of the wall due to each ball? and (ii) the ratio of the magnitudes of the impulses imparted on the two balls by the wall?
