Question

1. 2 points each - circle the letter of the best answer.

a ball at the end of a string is being swung in a horizontal circle. what force is producing
the centripetal acceleration of the ball?
a) gravity
b) the balls normal force
c) tension in string
d) air resistance
which one of the following statements concerning the two \gravitational constants\ g, the
universal gravitational constant, and g, the magnitude of the acceleration due to gravity is true?
(a) the values of g and g depend on location.
(b) the values of g and g do not depend on location.
(c) the value of g is the same everywhere in the universe, but the value of g is not.
(d) the value of g is the same everywhere in the universe, but the value of g is not.
(e) the values of g and g are equal on the surface of any planet, but in general, vary with location
in the universe.
two point masses m and m are separated by a distance d. if the separation d remains
fixed and the masses are increased to the values 3m and 3m respectively, how does the
gravitational force between them change?
a) the force will be one - third as great.
b) the force will be one - ninth as great.
c) the force will be three times as great.
d) the force will be nine times as great.
e) it is impossible to determine without knowing the numerical values of m, m, and d.

Explanation:

Step1: Analyze the first question

When a ball is swung in a horizontal circle, the centripetal force is provided by the tension in the string. Gravity acts vertically downwards, the normal force (if any) is perpendicular to the surface (not relevant here as it's a horizontal circle in air), and air - resistance opposes the motion (not the centripetal force).

Step2: Analyze the second question

The universal gravitational constant \(G\) is a fundamental constant and has the same value everywhere in the universe. The acceleration due to gravity \(g=\frac{GM}{R^{2}}\) (where \(M\) is the mass of the planet and \(R\) is the radius of the planet) depends on the location (e.g., on different planets or at different altitudes on the same planet).

Step3: Analyze the third question

The gravitational force is given by \(F = G\frac{mM}{d^{2}}\). If \(m\) becomes \(3m\) and \(M\) becomes \(3M\), then the new force \(F'=G\frac{(3m)(3M)}{d^{2}} = 9G\frac{mM}{d^{2}}=9F\)

Answer:

1. C. Tension in string
2. (c) The value of \(G\) is the same everywhere in the universe, but the value of \(g\) is not.
3. c) The force will be nine times as great.