Block A of mass 4.0 kg is on a horizontal, frictionless tabletop and is placed against a spring of negligible massand spring constant 650 N m-1. The other end of the spring is attached to a wall. The block is pushed toward thewall until the spring has been compressed a distance x, as shown above. The block is released and follows thetrajectory shown, falling 0.80 m vertically and striking a target on the floor that is a horizontal distance of 1.2 mfrom the edge of the table. Air resistance is negligible

(a) Calculate the time elapsed from the instant block A leaves the table to the instant it strikes the floor.

(b) Calculate the speed of the block as it leaves the table.(c) Calculate the distance x the spring was compressed.

Block B, also of mass 4.0 kg, is now placed at the edge of the table. The spring is again compressed a distance x,and block A is released. As it nears the end of the table, it instantaneously collides with and sticks to block B. The blocks follow the trajectory shown in the figure below and strike the floor at a horizontal distance d from the edge of the table.

(d) Calculate d if x is equal to the value determined in part (c).(e) Consider the system consisting of the spring, the blocks, and the table. How does the

total mechanical energy E2 of the system just before the blocks leave the table compare to the total mechanical energy E1 of the system just before block A is released?E2 < E1 E2 = E1 E2 > E1

Justify your answer

An open –ended U –tube of uniform cross sectional area contains water (1 g/cm3) standing initially 20 cm from the bottom in each arm. An immiscible liquid of density 4.0 g/cm3 is added to one arm until a layer 5 cm high forms, as shown. The ratio h1 / h2 of the heights of the liquid in the two arms

(1) 3 : 1 (2) 5 : 2 (3) 2 : 1 (4) 3 : 2 (5) 1 : 1

(2) A simple pendulum is taken from the equator to the pole. Its period (3) (a) decreases (b) increases (4) (c) remains the same (5) (d) decreases and then increases (6) (e) becomes infinity.

(7)

Three forces act on an object. If the object is in translational equilibrium, which of the following must

be true?

I. The vector sum of the three forces must equal zero.

II. The magnitudes of the three forces must be equal.

III. All three forces must be parallel.

(1) I only (2) II only (3) I and III only (4) II and III only (5) I, II, and III

20. Figure shows a uniform square of plate from which the part XBYA has been removed. If the moment of inertia of the plate around axes perpendicular to the plate C and through the points A,B, and C are IA, IB, and IC respectively. Then

(1) IA = IB = IC (2) IA, = IB IC (3) IA IB IC

(4) IA IC IB (5) IA IC IB

C

X A

B Y

21. Consider the following statements made regarding the action force and the reaction force,

A They are equal in magnitude

B They act on the same object

C They are opposite in direction to each other.

Of the above statements

(1) Only A is true (2) Only B is true (3) Only A and B are true (4) Only A and C are true (5)

All A, B and C are true.

22. A cricket bat is cut at the location of its center of mass as shown. Then

(1) the two pieces will have the same mass (2) the bottom piece will have larger mass (3) the handle piece will have larger mass (4) mass of handle piece is double the mass of bottom piece (5) cannot say

23. Two masses M and M / 2 are joined together by means of light inextensible string passed over a frictionless pulley as shown in the figure. When the bigger mass is released, the small one will ascent with an acceleration of

(1) g/3 (2) 3g/2 (3) g / 2 (4) g (5) g/4

24. Angular momentum of a system is

(A) Conserved only when the resultant force on it is zero(B) In the same direction as its angular velocity(C) Independent of the mass distribution of the system

Of the above statements

(1) Only A is true (2) Only B is true (3) Only C is true (4) Only B and C are true(5) All A, B and C are true.

16. Two rigid bodies P and Q are rotating about the same fixed axis and have angular velocities

ωP and ωQ and angular momentum Lp and LQ respectively. If the values of the ratio and are

1:2 and 2:3 respectively, the value of is

(1) (2) (3) (4) (5)17. The figure above shows a cart of mass M accelerating to the right with a block of mass m held to the front surface only by friction. The coefficient of friction between the surfaces is m .What is the minimum acceleration a of the cart such that the block will not fall

(1) µg (2) g / µ (3)

(4) (5)

18. A ball of mass m with speed u strikes a wall at an angle q with the normal, as shown above. It then rebounds with the same speed and at the same angle. The impulse delivered by the ball to the wall is

(1) zero(2) mu sinθ(3) mu cosθ(4) 2mu sinθ(5) 2mu cosθ

19. For a particle executing SHM, the displacement x is given by x = A cos ωt. Identify thegraph which represents the variation of potential energy ( PE ) as a function of time t and displacement x.

(1) (2) (3) (4) (5)

25. A stone of mass m is attached to a string. The stone is made to rotate in a vertical circle of radius r, as shown. At the point where the stone is vertically above the centre of the circle, the stone has speed v. Which of the following expressions gives the tension in the string

(1) mg – mv2 / r (2) mv2 / r (3) mv2 / r - mg

(4) mv2/r + mg (5) 0

10. Three forces act on an object. If the object is in translational equilibrium, which of the following must be true

(A) The vector sum of the three forces must equal zero.

(B) The magnitude of the three forces must be equal

(C) All three forces must be parallel

(1) A only (2) B only (3) A and C only (4) B and C only (5) A , B and C

11. A student weighing 700 N climbs at constant speed to the top of an 8 m vertical rope in 10 s. The average power expended by the student to overcome gravity is most nearly

(1) 1.1 W (2) 87.5 W (3) 560 W (4) 875 W (5) 5,600 W

12. An object of mass m hanging from a spring of spring constant k oscillates with a certain frequency. What is the length of a simple pendulum that has the same frequency of oscillation

(1) mk / g (2) mg / k (3) kg / m (4) k / mg (5) g / mk

13. Water flows through the pipe shown above. At the larger end, the pipe has diameter D and the speed of the water is v1 . What is the speed of the water at the smaller end, where the pipe has diameter d

(1) V1 (2) v (3) v (4) v1 (5) v1

14. Acceleration Vs time graph of a particle moving in a straight line is a shown. If initially particle was at rest, then corresponding KE Vs time graph will be

(1) (2) (3) (4) (5)

15. The total mass of a bullet and a cannon is 300 kg. If the bullet of mass 10 kg is fired from the cannon , the recoil velocity of the cannon is 1.5 ms-1 . Calculate the velocity of the bullet when the bullet is fired.

(1) 43.5 ms-1 (2) 45.0 ms-1 (3) 50.0 ms-1 (4) 65.0 ms-1 (5) 68.5 ms-1

05. A satellite of mass M moves in a circular orbit of radius R at a constant speed v. Which of the following must be true

(A) The net force on the satellite is equal to mv2/R and is directed toward the center of the orbit.(B) The net work done on the satellite by gravity in one revolution is zero.(C) The angular momentum of the satellite is a constant.

(1) A only (2) C only (3) A and B only (4) B and C only (5) A , B and C

06. A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock as it leaves the thrower's hand at the edge of the building is υ0 .The time it takes the rock to travel from the edge of the building to the ground is

(1) (2) h / v0 (3) h v0 / g (4) 2 h / g (5)

07. Two objects having the same mass travel toward each other on a flat surface, each with a speed of 10 meter per second relative to the surface. The objects collide head-on and are reported to rebound after the collision, eachwith a speed of 20 meters per second relative to the surface. Which of the following assessments of this report is most accurate

(1) Momentum was not conserved, therefore the report is false.(2) If potential energy was released to the objects during the collision, the report could be true.(3) If the objects had different masses, the report could be true.(4) If the surface was inclined, the report could be true.(5) If there was no friction between the objects and the surface, the report could be true.

08. An open –ended U –tube of uniform cross sectional area contains water (1 g/cm3) standing initially 20 cm from the bottom in each arm. An immiscible liquid of density 4.0 g/cm3 is added to one arm until a layer 5 cm high forms, as shown. The ratio h1 / h2 of the heights of the liquid in the two arms

(1) 3 : 1 (2) 5 : 2 (3) 2 : 1 (4) 3 : 2 (5) 1 : 1

09. Block A of mass 2 kg is placed over block B of mass 8 kg. The combination is placed over a rough horizontal surface. Coefficient of friction between B and the floor is 0.5. Coefficient of friction between A and B is 0.4. A horizontal force of 10 N is applied on block B. The force of friction between A and B is

(1) 20 N  (2)  50 N (3)  40 N (4)  100 N (5) zero

ISIPATHANA COLLEGE COLOMBO 05

fN!;sl úoHdj Ingsjpftpay; IPhysics I

One hourGrade 12 Term Test

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01. The Bernoulli’s equation is given by P + ½ d v2 + dgh = constant. The quantity dv2/2 has the same unit as those of

(1) Impulse (2) strain (3) pressure (4) force (5) momentum

02. The period of a simple pendulum is given by T = 2π where the letters have

usual meanings. The dimensional formula of (gT2/l) is

(1) [MLT] (2) [M0L0T0] (3) [ML-1T-1] (4) [M-1L-1T-1] (5) [ML-1T]

03. Vernier caliper is used to measure the depth of a tube. The depth is measured as

(1) 3.03 cm (2) 3.13 cm (3) 3.23 cm(4) 3.33 cm (5) 3.73 cm

04. A plane 5 meters in length is inclined at an angle of 37°, asshown. A block of weight 20 N is placed at the top of the plane and allowed to slide down. The magnitude of the normal force exerted on the block by the plane is most nearly

(1) l0 N (2) 12N (3) l6 N (4) 20 N (5) 33 N