Answer:
v = 1.32 10² m
Explanation:
In this case we are going to use the universal gravitation equation and Newton's second law
F = G m M / r²
F = m a
In this case the acceleration is centripetal
a = v² / r
The force is given by the gravitational force
G m M / r² = m v² / r
G M/r = v²
Let's calculate the mass of the planet
M = v² r / G
M = (1.75 10⁴)² 5.00 10⁶ / 6.67 10⁻¹¹
M = 2.30 10²¹ kg
With this die we clear the equation to find the orbit of the second satellite
v = √ G M / r
v = √ (6.67 10⁻¹¹ 2.30 10²¹ / 8.75 10⁶)
v = 1.32 10² m
The object takes 0.5 seconds to complete one rotation, so its rotational speed is 1/0.5 rot/s = 2 rot/s.
Convert this to linear speed; for each rotation, the object travels a distance equal to the circumference of its path, or 2<em>π</em> (1.2 m) = 2.4<em>π</em> m ≈ 7.5 m, so that
2 rot/s = (2 rot/s) • (2.4<em>π</em> m/rot) = 4.8<em>π</em> m/s ≈ 15 m/s
thus giving it a centripetal acceleration of
<em>a</em> = (4.8<em>π</em> m/s)² / (1.2 m) ≈ 190 m/s².
Then the tension in the rope is
<em>T</em> = (50 kg) <em>a</em> ≈ 9500 N.
Answer:
Capacitance, C = 26.1 picofarad
Explanation:
It is given that,
Side of square, x = 4.3546 cm = 0.043546 m
Distance between electrodes, d = 0.6408 mm = 0.0006408 m
Voltage, V = 73.68 V
Capacitance of parallel plates is given by :
or
C = 26.1 picofarad
So, the capacitance of the capacitor is 26.1 picofarad. Hence, this is the required solution.
