Question: What is the dimension of the gravitational constant G?
Options:
M^-1L^3T^-2
M^1L^3T^-2
M^1L^2T^-2
M^0L^0T^0
Correct Answer: M^-1L^3T^-2
Solution:
The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
What is the dimension of the gravitational constant G?
Practice Questions
Q1
What is the dimension of the gravitational constant G?
M^-1L^3T^-2
M^1L^3T^-2
M^1L^2T^-2
M^0L^0T^0
Questions & Step-by-Step Solutions
What is the dimension of the gravitational constant G?
Step 1: Understand that the gravitational constant G is used in the formula for gravitational force, which is F = G(m1*m2)/r^2.
Step 2: Identify the variables in the formula: F is force, m1 and m2 are masses, and r is the distance between the two masses.
Step 3: Recall the dimensions of each variable: Force (F) has dimensions of [MLT^-2], mass (m) has dimensions of [M], and distance (r) has dimensions of [L].
Step 4: Substitute the dimensions into the formula: G = F * r^2 / (m1 * m2).
Step 5: Replace F with its dimensions: G = ([MLT^-2] * [L^2]) / ([M] * [M]).
Step 6: Simplify the expression: G = [MLT^-2 * L^2] / [M^2] = [ML^3T^-2] / [M^2].
Step 7: Further simplify: G = [M^(1-2)L^3T^-2] = [M^-1L^3T^-2].
Step 8: Conclude that the dimension of the gravitational constant G is [M^-1L^3T^-2].
No concepts available.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
