15. Life time of a particle is 2.2 x 10 s in a frame in which...

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15. Life time of a particle is 2.2 x 10 s in a frame in which it is at rest. Calculate the average distance it will travel in vacuo before decaying if its speed is (a) 0.9 c, (b) 099 c and (c) 0.999 c. (Ans. (a) 1.36 km; (b) 4.6 km; (c) 14.5 km) 16. What is the velocity of a metre scale if its length is observed to be shortened by a centimeter? (Ans. v = 0.141c) 17. An observer O holds a metre scale at an angle of 30° with respect to the positive X'-axis. O is moving in the positive X- X' direction with a velocity v relative to observer O. What is the value of v if the metre scale makes an angle of 45° with respect to X-axis of 0. What is the length of the metre scale as measured by O? (Ans, y = 0,816 c. L= 0 707 m) 15. Life time of a particle is 2.2 x 10 s in a frame in which it is at rest. Calculate the average distance it will travel in vacuo before decaying if its speed is (a) 0.9 c, (b) 099 c and (c) 0.999 c. (Ans. (a) 1.36 km; (b) 4.6 km; (c) 14.5 km) 16. What is the velocity of a metre scale if its length is observed to be shortened by a centimeter? (Ans. v = 0.141c) 17. An observer O holds a metre scale at an angle of 30° with respect to the positive X'-axis. O is moving in the positive X- X' direction with a velocity v relative to observer O. What is the value of v if the metre scale makes an angle of 45° with respect to X-axis of 0. What is the length of the metre scale as measured by O? (Ans, y = 0,816 c. L= 0 707 m)

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