The upper end of a wire of length 5 m is fixed to a ceiling and a 20 kg mass is attached at its lower end. If the wire makes an angle 60° with the horizontal, then the moment of force with respect to the upper end of the wire is (Acceleration due to gravity = 10 m s-2)

The correct answer is Option 4. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q89 – AP-EAMCET 2025

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Home Physics Rotational MotionQuestion #428

The upper end of a wire of length

5 m

is fixed to a ceiling and a

20 kg

mass is attached at its lower end. If the wire makes an angle

60^{\circ}

with the horizontal, then the moment of force with respect to the upper end of the wire is (Acceleration due to gravity =

10 {m s}^{- 2}

)

Clue 1 of 3: Understanding Torque

Torque is the rotational equivalent of force, causing an object to rotate about an axis. It depends on the magnitude of the force, the distance from the pivot to the point of force application, and the angle between the force and the position vector.

🧠 Full Solution Path

Step 1: Identify Force and Lever Arm✦ Active

The force acting on the lower end of the wire is the weight of the mass. The pivot point is the upper end of the wire. The length of the wire acts as the lever arm.

F = m g

F = 20 kg \times 10 {m s}^{- 2} = 200 N

r = L = 5 m

💡 Teacher's Secret Hint

Ensure you use the correct value for acceleration due to gravity ( $g$ ) as specified in the problem, which is $10 {m s}^{- 2}$ in this case, not the standard $9.8 {m s}^{- 2}$ .

Step 2: Calculate the Angle for Torque○ Expand

The wire makes an angle of $60^{\circ}$ with the horizontal. The force (weight) acts vertically downwards. The angle $ϕ$ between the position vector (along the wire) and the force vector (vertically downwards) is the complement of the angle with the horizontal.

ϕ = 90^{\circ} - angle with horizontal

ϕ = 90^{\circ} - 60^{\circ} = 30^{\circ}

💡 Teacher's Secret Hint

It's crucial to correctly identify the angle $ϕ$ in the torque formula. It's the angle between the lever arm vector and the force vector, not necessarily the angle given directly in the problem statement.

Step 3: Apply the Torque Formula○ Expand

Now, substitute the calculated force, lever arm, and angle into the torque formula.

τ = r F \sin ϕ

τ = (5 m) (200 N) \sin (30^{\circ})

τ = 1000 N m \times \frac{1}{2}

τ = 500 N m

💡 Teacher's Secret Hint

Remember that $\sin (30^{\circ}) = 0.5$ . Double-check your trigonometric values.

Step 4: Select the Correct Option○ Expand

The calculated moment of force is $500 N m$ , which corresponds to option 4.

💡 Teacher's Secret Hint

Always review the units of your final answer to ensure they are consistent with the quantity being calculated (e.g., N m for torque).

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Physics Question 89 – AP-EAMCET 2025

Clue 1 of 3: Understanding Torque

🧠 Full Solution Path