Physics 2010 JAMB Past Questions - Question 8: A bob of weight of 0.1 N hangs from a massless string of length 50 cm .A variable horizontal force which increases from zero is applied to pull the bob until the string makes an angle of 60° with the vertical. The work done is

Correct Answer

B

Explanation

To find the work done in this scenario, you can break it down into two components: the work done against gravity as the bob is lifted and the work done to change the direction of the bob's velocity.

1. Work done against gravity:
The weight of the bob is 0.1 N, and it acts vertically downward. As the bob is lifted, you are doing work against gravity. The work done against gravity is given by the formula:

Work_gravity = force * distance

Here, the force is the weight (0.1 N) and the distance is the vertical height the bob is lifted. Since the string makes an angle of 60 degrees with the vertical, the height is given by:

Height = 0.5 * 50 cm * sin(60°) = 25 cm * √3 / 2 = 25√3 cm = 0.25√3 meters

So, the work done against gravity is:

Work_gravity = 0.1 N * 0.25√3 m

2. Work done to change the direction of the bob's velocity:
As the string is pulled horizontally, a horizontal force is applied to change the direction of the bob's velocity. Work is done to change the direction of the velocity, and this work is equal to the kinetic energy gained by the bob.

The kinetic energy gained is given by:

KE = 1/2 * m * v^2

Where:
- m is the mass of the bob (you haven't provided this, but you can calculate it using the weight and the acceleration due to gravity).
- v is the final velocity of the bob.

Since the bob is initially at rest, the work done to change its velocity is equal to its kinetic energy:

Work_velocity = KE

Now, to calculate the final velocity, you can use the conservation of energy:

Initial energy (all gravitational potential) + Work_velocity = Final energy (part gravitational potential and part kinetic)

0 (initial kinetic energy) + Work_velocity = m * g * h + 1/2 * m * v^2

Solve for v:

Work_velocity = m * g * h + 1/2 * m * v^2

Work_velocity = m * g * h (since the initial kinetic energy is zero)

v^2 = (2 * Work_velocity) / m

v = sqrt((2 * Work_velocity) / m)

3. Now, you need to calculate the mass of the bob:

Weight (W) = m * g

Where W is the weight (0.1 N) and g is the acceleration due to gravity (approximately 9.81 m/s²).

m = W / g

4. Calculate the final velocity (v).

5. Calculate the work done to change the direction of the bob's velocity (Work_velocity) using the formula mentioned earlier.

6. The total work done is the sum of the work done against gravity and the work done to change the direction of the bob's velocity:

Total Work = Work_gravity + Work_velocity

Calculate the values of Work_gravity, Work_velocity, and then add them to find the total work done.