Physics 2008 JAMB Past Questions - Question 5: A force F is required to keep a 5kg mass moving round a cycle of radius 3.5m at a speed of 7ms-¹ What is the speed if the force is tripled?

Correct Answer

C

Explanation

To find the speed of the 5 kg mass when the force is tripled, you can use the concept of centripetal force. The centripetal force required to keep an object moving in a circle is given by:

F = (m * v^2) / r,

where:
F is the centripetal force,
m is the mass of the object (5 kg in this case),
v is the velocity of the object (initially 7 m/s),
r is the radius of the circle (3.5 m in this case).

We can solve for v in the initial situation:

F = (5 kg * (7 m/s)^2) / 3.5 m
F = (5 * 49) / 3.5
F = 70 N.

Now, if the force is tripled, the new force (3F) will be:

3F = 3 * 70 N
3F = 210 N.

To find the new speed (v_new), we can use the same formula:

3F = (5 kg * (v_new^2)) / 3.5 m.

Now, solve for v_new:

v_new^2 = (3F * 3.5 m) / 5 kg
v_new^2 = (210 N * 3.5 m) / 5 kg
v_new^2 = 147 m^2/s^2.

To find v_new, take the square root of both sides:

v_new = √(147 m^2/s^2)
v_new ≈ 12.12 m/s.

So, when the force is tripled, the speed of the 5 kg mass will be approximately 12.12 m/s.