Answer:
(a) r = 1.062·R
= 
(b) r = 
(c) Zero
Explanation:
Here we have escape velocity v
given by
and the maximum height given by

Therefore, when the initial speed is 0.241v
we have
v =
so that;
v² =
v² = 
is then

Which gives
or
r = 1.062·R
(b) Here we have

Therefore we put
in the maximum height equation to get

From which we get
r = 1.32·R
(c) The we have the least initial mechanical energy, ME given by
ME = KE - PE
Where the KE = PE required to leave the earth we have
ME = KE - KE = 0
The least initial mechanical energy to leave the earth is zero.
Answer:
option (b)
Explanation:
Let the resistance of each resistor is R.
In series combination,
The effective resistance is Rs.
rs = r + R + R + .... + n times = NR
Let V be the source of potential difference.
Power in series
Ps = v^2 / Rs = V^2 / NR ..... (1)
In parallel combination
the effective resistance is Rp
1 / Rp = 1 / R + 1 / R + .... + N times
1 / Rp = N / R
Rp = R / N
Power is parallel
Rp = v^2 / Rp = N V^2 / R ..... (2)
Divide equation (1) by equation (2) we get
Ps / Pp = 1 / N^2
Answer:
D. The period would decrease by sqrt (2)
Explanation:
The period of a mass-spring system is given by:

where
m is the mass
k is the spring constant of the spring
If the spring constant is doubled,
k' = 2k
So the new period will be

So the correct answer is
D. The period would decrease by sqrt (2)
To determine the diameter of the earth in metres first multiply the original value by 2.
6378 X 2 = 12 756 km.
Then convert km - m
1 km = 1000 m
12 756 km = ? m
12 756 • 1000 = 12 756 000 = 12 756 000 m or 1.2756 X 10 ^ 7 m
The final solution for the diameter is 1.2756 X 10 ^ 7 m.