Q#1
Galileo was punished by the Church for teaching that the sun is stationary and the earth moves around it. His opponents held the view that the earth is stationary and the sun moves around it. If the absolute motion has no meaning, are the two viewpoints not equally correct or equally wrong?Answer:
As far as absolute motion is concerned the two viewpoints are equally correct or equally wrong. Galileo is true only if the point of reference is chosen away from the solar system like another star.
When a particle moves with constant velocity, its average velocity, its instantaneous velocity, and its speed are all equal. Comment on this statement.
Answer:
A particle moving with constant velocity move an equal distance in equal time whatever the magnitude of time taken to compare. So the ratio of distance to time is always constant. So the average velocity (which is the ratio of total displacement to total time), instantaneous velocity (Which is the ratio of infinitesimal distance covered to infinitesimal time at the instant) and speed (which is the ratio of distance covered to the time taken) are all equal.
A car travels at a speed of 60 km/hr due north and other at a speed of 60 km/hr due east. Are the velocities equal? If no, which one is greater? If you find any of the questions irrelevant, explain.
Answer:
The velocities are not equal because velocity is a vector quantity having both magnitude and direction. In this case, both are equal in magnitude but not in direction. The question "which one is greater?" is irrelevant because two vectors can only be compared if they have the same direction.
A ball is thrown vertically upward with a speed of 20 m/s. Draw a graph showing the velocity of the ball as a function of time as it goes up and then comes back.
Answer:
When the ball goes up its velocity at any instant is given by
v = u – gt, here u = 20 m/s, let g = 10 m/s².
This gives v = 20 – 10t; on the time-velocity graph, it is an equation of a straight line with an intercept of 20 m/s on the Y-axis (along which velocity is plotted) and gradient of (-10).
Let us find time t for the v to become zero,
0 = 20 – 10t
t = 2 s
so, this straight line will touch the X-axis (along which time is plotted) at t = 2 s.
When the ball goes down its velocity at any instant reverses its direction ie it becomes negative and in the next 2 s it comes back to the initial point with 20 m/s.
Q#5
The velocity of a particle is towards the west at an instant. Its acceleration is not towards the west, not towards the east, not towards the north and not towards the south. Give an example of this type of motion. Answer:
Consider a case when a particle is thrown towards the west at an angle with horizontal. At the highest point of its trajectory, its instantaneous velocity is towards the west but the acceleration is not towards the west, not towards the east, not towards the north and not towards the south. In fact, its acceleration is vertically downwards due to gravity.
At which point on its path a projectile has the smallest speed?
Answer:
At the highest point on its path a projectile has the smallest speed.
Two particles A and B start from rest and move for equal time on a straight line. The particle A has an acceleration a for the first half of the total time and 2a for the second half. The particle B has an acceleration 2a for the first half and a for the second half. Which particle has covered a larger distance?
Answer:
Let (2t) be the total time for which the particles move, vA and vB the velocities of particle A and B after the first half of the total time. From the equation v = u + at,
For particle A, u = 0, vA = at
using equation s = ut + ½at²
Total distance traveled by particle A
dA = [ut + ½ at²] + [vAt + ½(2)at²]
dA = (0 + ½at²) + (at.t + at²) = ½at² + 2at²
dA = 2.5at²
For particle B, vB = 0 + 2at = 2at,
So total distance traveled by particle B
dB = [ut + ½(2)at²] + (vBt + ½at²)
= (0 + at²) + (2at.t + ½at²)
dB = at² + 2at² + ½at² = 3at² + ½at²
= 3.5at²
Comparing both it is clear that particle B covered a larger distance.
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