Centripetal Force and ball of string

[merlin.matt]

Hello, could someone look over my answer? I am not very confident I did the problem correctly.

Homework Statement

A 76-kg ball is tied to one end of a massless string of length The other end of the string is tied to a nail in the center of a table. The ball is set into uniform circular motion around the nail, and the tension in the string is 51 N. How long does the ball take to make one complete revolution? Assume friction with the table is negligible.
A. 8.7 s
B. 9.5 s
C. 7.0 s
D. 8.1 s

Homework Equations

T= m*a
a = V^2/R
V= 2*pi*R/T

The Attempt at a Solution

T = ma
51=76*a
a = 51/76
a= 0.67

a= V^2/R
V= √a*r
V= √0.67*1.3
V= 0.93

V = 2*π*R/t
t = 2*π*R/V
t= 2*π*1.3/0.93
t= 8.7 s

 

[Panphobia]

Reply

T = mv^2/r
51 = 76v^2/1.3
v =.934

ω = v/r
ω = 0.934/1.3
= 0.72

0.72 = 2*∏*r/(r*t)
t = (2*∏)/0.72
= 8.7s

Yes you were right.