Two persons are holding a rope of negligible mass horizontally. A 20 k

Two persons are holding a rope of negligible mass horizontally. A 20 kg mass is attached to the rope at the midpoint; as a result the rope deviates from the horizontal direction. The tension required to completely straighten the rope is (g = 10 m/s²)

Join Our Telegram Channel

200 N

20 N

10 N

infinitely large

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CDS-2 – 2018

Download PDF Attempt Online

When a mass is attached to the midpoint of a horizontally held rope, the rope sags downwards due to the weight of the mass (W = mg). The tension in the rope acts along the direction of the rope segments on either side of the mass. For the rope to be in equilibrium, the vector sum of the two tensions and the weight must be zero. If the rope is perfectly horizontal, the tension vectors would have only horizontal components (neglecting the mass of the rope itself). However, the weight of the attached mass acts vertically downwards. To balance this downward force, there must be an equal and opposite upward force provided by the vertical components of the tension in the rope. As the rope approaches a perfectly horizontal state, the angle (θ) it makes with the horizontal approaches zero. The vertical component of the tension in each half of the rope is T * sin(θ), where T is the tension. The total upward vertical force is 2 * T * sin(θ). To balance the weight W, 2 * T * sin(θ) = W. If the rope is to be perfectly straight and horizontal (θ = 0), then sin(θ) = sin(0) = 0. For 2 * T * sin(θ) to equal the non-zero weight W (20 kg * 10 m/s² = 200 N), the tension T must tend towards infinity as sin(θ) tends towards zero. Thus, an infinitely large tension is required to completely straighten the rope.

– Static equilibrium requires the net force in all directions to be zero.
– When a mass hangs from a rope, the weight acts vertically downwards.
– Tension in the rope must have a vertical component to balance the weight.
– For a nearly horizontal rope, the angle with the horizontal is very small.
– As the angle approaches zero, the sine of the angle approaches zero, requiring tension to approach infinity to provide a non-zero vertical force.

This scenario represents a classic physics problem illustrating the vector resolution of forces and the limit as an angle approaches zero. In any real-world scenario, the rope will always sag slightly, having a non-zero angle, because no rope can withstand infinite tension.

More similar MCQ questions for Exam preparation:-