Question

A sling is being rotated at the rate of 92 rpm. What will the length of the sling have to be so that the speed of the object at the end will be 46 meters per second? (in meters)

A) 2 meters
B) 4 meters
C) 8 meters
D) 23 meters

Answer 1

To find the length of the sling, use the formula v = rω and solve for r. Substituting the given values, the length of the sling is approximately 8 meters. The correct option is C.

Step-by-step explanation:

To determine the length of the sling, we need to use the formula for linear speed in circular motion:

v = rω

where v is the linear speed, r is the radius or length of the sling, and ω is the angular velocity in radians per second.

Given that the angular velocity is 92 revolutions per minute, we need to convert it to radians per second by multiplying it by 2π/60, since there are 2π radians in a revolution and 60 seconds in a minute.

Then we can rearrange the formula to solve for r:

r = v/ω

Substituting in the given values of v = 46 m/s and ω = (92*2π/60) radians/s, we can calculate the length of the sling.

After evaluating the expression, we find that the length of the sling should be approximately 8 meters.