Question

A rock is suspended from a string; and it accelerates downward. Which one of the following statements concerning the tension in the string is true?
A) The tension points downward.
B) The tension is less than the weight of the rock.
C) The tension is equal to the weight of the rock.
D) The tension is greater than the weight of the rock. The tension is independent of the magnitude of the rock's acceleration.

Answer 1

Answer:

B) The tension is less than the weight of the rock.

Explanation:

When the rock is suspended from the string, forces acting on the rock are

$T$ = tension force in the string in upward direction

$F_{g}$ = Force of gravity on the rock in down direction

$m$ = mass of the rock

$a$ = acceleration of the rock

For the rock to accelerate in down direction, force equation can be given as

$F_{g} - T = ma$

Rearranging the equation , we get

$T = F_{g} - ma$

Clearly

$T < F_{g}$

So the correct statement is

B) The tension is less than the weight of the rock.