**APEX INSTITUTE SCIENCE & MATHEMATICS**

**SUNDAY TEST**

- ABCD is a trapezium with AB||DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX)=ar (ACY).
- XY is a line parallel to side BC of a triangle ABC. If BE ||AC and CF||AB meet XY at E and F respectively, Show that ar ( ABE) = ar (ACF)
- P and Q are any two points lying on the sides DC and AD respectively of parallelogram ABCD. Show that ar (APB) =ar (BQC).
- If E, F, G and H are respectively the mid-points of the sides of a parallelogram ABCD, show that ar (EFGH) =1/2 ar (ABCD).
- ABCD is a parallelogram, AE DC and CF AD. If AB =16cm, AE=8cm and CF=10cm, find AD.

6. Three balls A, B and C are kept in a straight line. The separation between A and C is 1 m, and B is placed at the midpoint between them. The masses of A, B, C are 100 g, 200 g and 300 g respectively. Find the net gravitational force on (a) A, (b) B, and (c) C.

7. A particle of mass m1 is kept at x = 0 and another of mass m2 at x = d. When a third particle is kept at x = d/4, it experiences no net gravitational force due to the two particles. Find m2/m1.

8. The acceleration due to gravity near the earth's surface is 9.8 m/s2, and the earth's radius is 6,400 km. From this data calculate the mass of the earth. Use any universal constant if required.

9. Two particles of mass 200 g each are placed at a separation of 10 cm. Assume that the only forces acting on them are due to their gravitational attraction. Find the acceleration of each when they are allowed to move.

10. A particle weighs 120 N on the surface of the earth. At what height above the earth's surface will its weight be 30 N? Radius of the earth = 6,400 km.

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