What happens to the centripetal force when mass is tripled, speed is halved, and radius remains unchanged?

To find out how the centripetal force changes when an object’s mass is tripled while its speed is halved and the radius stays constant, we can start with the formula for centripetal force:

F = (m * v²) / r

Where:

• F is the centripetal force
• m is the mass of the object
• v is the speed of the object
• r is the radius of the circle

If we let:

• The original mass be m
• The original speed be v
• The radius be r

The initial centripetal force can be expressed as:

F_initial = (m * v²) / r

Now, according to the conditions of the problem, the mass becomes 3m, the speed becomes v/2, and the radius still is r. Plugging these values into the centripetal force formula gives:

F_final = (3m * (v/2)²) / r

Calculating the new speed squared:

(v/2)² = v² / 4

Now, substituting this back in:

F_final = (3m * (v² / 4)) / r = (3m * v²) / (4r)

Now we can express the final force in relation to the initial force:

F_final = (3/4) * (m * v²) / r = (3/4) * F_initial

This tells us that the final centripetal force is multiplied by a factor of 3/4. Therefore, the correct choice from the options provided is (b) 3/4.