Answer:
Ratio of length will be 
Explanation:
We have given time period of the pendulum when length is
is 
And when length is
time period 
We know that time period is given by

So
----eqn 1
And
-------eqn 2
Dividing eqn 2 by eqn 1

Squaring both side

Thermal energy Thermal energy <span>Thermal energy</span>
Answer:
Option A applies.
A. Greater than its escape speed from the mass within the volume
Explanation:
Here it is mentioned that the spherical volume is large enough for the space to be considered as homogeneous. Also, the pressure within the volume is negligible, so that will not result into the re collapse of the Universe. Now as per our knowing, Hubble's Law relates the average speed of the particle to the distance R between the Earth and the particle. So, if the particle's speed is greater than it's escape speed from the mass within the volume, then the Universe is bound to re collapse back again. Option A applies.
Answer:
Explanation:
Initial kinetic energy of M = 1/2 M vi²
let final velocity be vf
v² = u² + 2a s
vf² = vi² + 2 (F / M) x D
Kinetic energy
= 1/2 Mvf²
= 1/2 M ( vi² + 2 (F / M) x D
1/2 M vi² + FD
Ratio with initial value
1/2 M vi² + FD) / 1/2 M vi²
RK = 1 + FD / 2 M vi²