Concept explainers
(a)
To Find:The acceleration of each mass.
(a)
Explanation of Solution
Given:
Smaller mass,
Larger mass,
Distance between two smaller masses,
Distance between smaller mass and larger mass,
Formula used:
Gravitational force between two bodies having mass m and M , d distance away is:
G is the gravitational constant.
Newton’s second law of motion:
Calculation:
Acceleration of smaller mass (m):
Acceleration of larger mass (m):
Conclusion:
Thus, mass m accelerates with
(b)
To Find: The time required by each mass to move by
(b)
Explanation of Solution
Given:
Smaller mass,
Larger mass,
Distance between two smaller masses,
Distance between smaller mass and larger mass,
Distance moved by each mass,
mass m accelerates with
mass M accelerates with
Formula used:
Second equation of motion:
Where, u is the initial velocity, t is the time and a is the acceleration.
Calculation:
Consider that each mass is initially at rest. Then,
For mass m:
For mass M:
Conclusion:
Thus, mass mmoves in
(c)
To Find: The angle by which the rotates in the given time interval.
(c)
Explanation of Solution
Given:
Smaller mass,
Larger mass,
Distance between two smaller masses,
Distance between smaller mass and larger mass,
Distance moved by each mass,
Mass m accelerates with
Mass M accelerates with
Mass m moves in
Formula used:
Second equation of rotational motion:
Where,
Angular acceleration is related to linear acceleration as:
Where, a is the linear acceleration and r is the radius.
Calculation:
Initially, the rod is at rest. So,
Conclusion:
Thus, the rod rotates by an angle of
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- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University