Advertisements
Advertisements
Question
A person travels by a car at a speed of 180 km h−1. It takes exactly 10 hours by his wristwatch to go from the station A to the station B. (a) What is the rest distance between the two stations? (b) How much time is taken in the road frame by the car to go from the station A to the station B?
Solution
Given:-
Speed of car, v = 180 km/hr = 50 m/s
Time, t = 10 h
(a) Let the rest distance be L0.
Apparent distance is given by
\[L' = L_0 \sqrt{1 - v^2 / c^2}\]
Apparent distance, L' = 10 × 180 = 1800 km = 18 × 105 m
Now,
\[18 \times {10}^5 = L_0 \sqrt{1 - \frac{\left( 50 \right)^2}{\left( 3 \times {10}^8 \right)^2}}\]
\[L_0 = \left( 18 \times {10}^5 + 25 \times {10}^{- 9} \right) m\]
Thus, the rest distance is 25 nm more than 1800 km.
(b) Let the time taken by the car to cover the distance in the road frame be t. Then,
\[t = \frac{1 . 8 \times {10}^5 + 25 \times {10}^{- 9}}{50}\]
\[ = 0 . 36 \times {10}^5 + 5 \times {10}^{- 8} \]
`= 10 "hours" + 0.5 "ns"`
APPEARS IN
RELATED QUESTIONS
A uniformly moving train passes by a long platform. Consider the events 'engine crossing the beginning of the platform' and 'engine crossing the end of the platform'. Which frame (train frame or the platform frame) is the proper frame for the pair of events?
An object may be regarded to be at rest or in motion depending on the frame of reference chosen to view the object. Because of length contraction it would mean that the same rod may have two different lengths depending on the state of the observer. Is this true?
An experimenter measures the length of a rod. Initially the experimenter and the rod are at rest with respect to the lab. Consider the following statements.
(A) If the rod starts moving parallel to its length but the observer stays at rest, the measured length will be reduced.
(B) If the rod stays at rest but the observer starts moving parallel to the measured length of the rod, the length will be reduced.
An experimenter measures the length of a rod. In the cases listed, all motions are with respect to the lab and parallel to the length of the rod. In which of the cases the measured length will be minimum?
Two events take place simultaneously at points A and B as seen in the lab frame. They also occur simultaneously in a frame moving with respect to the lab in a direction _________________ .
An aeroplane travels over a rectangular field 100 m × 50 m, parallel to its length. What should be the speed of the plane so that the field becomes square in the plane frame?
The rest distance between Patna and Delhi is 1000 km. A nonstop train travels at 360 km h−1. (a) What is the distance between Patna and Delhi in the train frame?
(b) How much time elapses in the train frame between Patna and Delhi?
According to the station clocks, two babies are born at the same instant, one in Howrah and other in Delhi. (a) Who is elder in the frame of 2301 Up Rajdhani Express going from Howrah to Delhi? (b) Who is elder in the frame of 2302 Dn Rajdhani Express going from Delhi to Howrah.
Two babies are born in a moving train, one in the compartment adjacent to the engine and other in the compartment adjacent to the guard. According to the train frame, the babies are born at the same instant of time. Who is elder according to the ground frame?
An electric bulb, connected to a make and break power supply, switches off and on every second in its rest frame. What is the frequency of its switching off and on as seen from a spaceship travelling at a speed 0.8c?
At what speed the volume of an object shrinks to half its rest value?
