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# At some moment, two giant planets … ## CBSE, JEE, NEET, CUET

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At some moment, two giant planets Jupiter and Saturn of the solar system are in the same line as seen from the earth. Find the total gravitational force due to them on a person of mass 50 kg on the earth. Could the force due to the planets be important? Mass of the Jupiter = 2 × 1027 kg Mass of the Saturn = 6 × 1026 kg The distance of Jupiter from the earth = 6.3 × 1011 m The distance of Saturn from the earth = 1.28 × 1012 m A bag of sugar weighs ‘w’ at a certain place on the equator. If this bag is taken to Antarctica, then will it weigh the same or more or less. Give a reason for your answer.

Sehajpreet Kaur 9 months ago

In Δ ABC, P and Q are the mid-points of sides AB and BC respectively. ∴ PQ || AC and PQ = 12 AC ( Using mid-point theorem) …..(1) In ΔADC, R and S are the mid - points of CD and AD respectively. ∴ RS || AC and RS = 12 AC ( Using mid-point theorem) …..(2) From equation (1) and (2) , we obtain PQ || RS and PQ = RS Since in quadrilateral PQRs, one pair of opposite sides is equal and parallel to each other , it is a parallelogram. Let the diagonals of rhombus ABCD intersect each other at point O. In Quadrilateral OMQN, MQ || ON (∵ PQ || AC) QN || OM (∵ QR || BD) Therefore, OMQN is a parallelogram. ∴∠MQN=∠NOM and ∠PQR=∠NOM However, ∠NOM=90∘ (Diagonals of a rhombus are perpendicular to each other) ∴∠PQR=90∘ Clearly , PQRS is a parallelogram having one of its interior angles as 90∘ Hence, PQRS is a rectangle.

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