To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.090 kg ball . . .?

Question

To measure the acceleration due to gravity on a distant planet, an astronaut hangs a 0.090 kg ball from the end of a wire. The wire has a length of 1.5 m and a linear density of 3.1 X 10^-4 kg/m. Using electronic equipment, the astronaut measures the time for a transverse pulse to travel the length of the wire and obtains a value of 0.066 s. The mass of the wire is negligible compared to the mass of the ball. Determine the acceleration due to gravity.

(My assumption is that gravity = 9.8 m/s; or gravity must also be solved for)

Answer 1

I believe that you can relate this problem as follows:

The ball is so massive compared to the wire you can assume that the mass of the ball doesn't move, and that it is caused to align radially to the gravitational field of the planet (this also ignores the mass of the spaceship).

Under these conditions, the velocity of a wave in the wire will obey the equation
v=sqrt(T/(m/L))
where T is the tension in the wire, L is the length, and m is the mass of the wire, so m/L is the linear density of the wire.

Since the mass of the wire is negligible, the tension is m*g of the ball, where g will be the gravitational acceleration of the planet.
Since L=v*t
and t=0.066, L=1.5
V=1.5/0.066

Building the rest of the equation
1.5/0.066=
sqrt(0.09*g/3.1x10^-4)

solving for g
g=(3.1x10-4/0.09)*
(1.5/0.066)^2

=1.8 m/s^2

j

Answer 2

wouldn't that supposed to be 1.18m/s^2 or 1.19m/s^2