Answer:
R2 = 300 Ohms
Explanation:
Let the two resistors be R1 and R2 respectively.
RT is the total equivalent resistance.
Given the following data;
R1 = 100 Ohms
RT = 75 Ohms
To find R2;
Mathematically, the total equivalent resistance of resistors connected in parallel is given by the formula;
Substituting into the formula, we have;
Cross-multiplying, we have;
75 * (100 + R2) = 100R2
7500 + 75R2 = 100R2
7500 = 100R2 - 75R2
7500 = 25R2
R2 = 7500/25
R2 = 300 Ohms
Given: Mass of earth Me = 5.98 x 10²⁴ Kg
Radius of earth r = 6.37 x 10⁶ m
G = 6.67 x 10⁻¹¹ N.m²/Kg²
Required: Smallest possible period T = ?
Formula: F = ma; F = GMeMsat/r² Centripetal acceleration ac = V²/r
but V = 2πr/T
equate T from all equation.
F = ma
GMeMsat/r² = Msat4π²/rT²
GMe = 4π²r³/T²
T² = 4π²r³/GMe
T² = 39.48(6.37 x 10⁶ m)³/6.67 x 10⁻¹¹ N.m²/Kg²)(5.98 x 10²⁴ Kg)
T² = 1.02 x 10²² m³/3.99 x 10¹⁴ m³/s²
T² = 25,563,909.77 s²
T = 5,056.08 seconds or around 1.4 Hour
Explanation:
Period P has units of seconds (s).
Length has units of meters (m).
Mass has units of kilograms (kg).
Acceleration has units of meters per second squared (m/s²).
Dimensional analysis:
s = √(m / (m/s²))
Therefore:
P = k √(L/g)
where k is a dimensionless constant.
Answer:
23.52 m/s
Explanation:
The following data were obtained from the question:
Time taken (t) to reach the maximum height = 2.4 s
Acceleration due to gravity (g) = 9.8 m/s²
Initial velocity (u) =..?
At the maximum height, the final velocity (v) is zero. Thus, we can obtain how fast the rock (i.e initial velocity)
was thrown as follow:
v = u – gt (since the rock is going against gravity)
0 = u – (9.8 × 2.4)
0 = u – 23.52
Collect like terms
0 + 23.52 = u
u = 23.52 m/s
Therefore, the rock was thrown at a velocity of 23.52 m/s.
