What is the dimension of the gravitational constant G?
Practice Questions
1 question
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
The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
Questions & Step-by-step Solutions
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Q
Q: What is the dimension of the gravitational constant G?
Solution: The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
Steps: 8
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].
