03%20-%20Description%20of%20Motion%20in%20Two%20and%20Three%20Dimensions

03%20-%20Description%20of%20Motion%20in%20Two%20and%20Three%20Dimensions

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- DESCRIPTION OF MOTION IN TWO AND THREE DIMENSIONS Page 1 ( Answers at the end of all questions ) 1 ) A particle is moving eastwards with a velocity of 5 ms - 1 . In 10 seconds the velocity changes to 5 ms - 1 northwards. The average acceleration in this time is ( a ) 1 / 2 ms - 2 towards north ( b ) 1 / √ 2 ms - 2 towards north - east ( c ) 1 / √ 2 ms - 2 towards north - west ( d ) zero [ AIEEE 2005 ] 2 ) An annular ring with inner and outer radii R 1 and R 2 is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, F 1 / F 2 is ( a ) 2 2 R 1 R ( b ) 1 R 2 R ( c ) 2 R 1 R ( d ) 1 [ AIEEE 2005 ] 3 ) A projectile can have the same range ‘R’ for two angles of projection. If ‘t 1 and ‘t 2 be the times of flights in the two cases, then the product of the two times of flights is proportional to ( a ) 1 / R 2 ( b ) R 2 ( c ) R ( d ) 1 / R [ AIEEE 2005, 2004 ] 4 ) A block is kept on a frictionless surface with angle of inclination α ’. The incline is given an acceleration ‘a’ to keep the block stationary. Then a is equal to ( a ) g cosec α ( b ) g / tan α ( c ) g tan α ( g ) g [ AIEEE 2005 ] 5 ) Which of the following statements is false for a particle moving in a circle with a constant angular speed ? ( a ) The velocity vector is tangent to the circle. ( b ) The acceleration vector is tangent to the circle. ( c ) The acceleration vector points to the centre of the circle. ( d ) The velocity and acceleration vectors are perpendicular to each other. [ AIEEE 2004 ] 6 ) If , then the angle between A and B is × = × A B B A ( a ) π ( b ) π / 3 ( c ) π / 2 ( d ) π / 4 [ AIEEE 2004 ] 7 ) A ball is thrown from a point with a speed v 0 at an angle of projection θ . From the same point and at the same instant, a person starts running at a constant speed v 0 / 2 to catch the ball. Will the person be able to catch the ball ? If yes, what should be the angle of projection ? ( a ) yes, 60 ° ( b ) yes, 30 ° ( c ) No ( d ) yes, 45 ° [ AIEEE 2004 ] 8 ) The coordinates of a moving particle at any time t are given by x = α t 3 and y = β t 3 . The
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03%20-%20Description%20of%20Motion%20in%20Two%20and%20Three%20Dimensions

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