Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 1]PhysicsNewton's Laws of Motion

A man has fallen into a ditch of width d , and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the figure. Assuming the force exerted by both friends is equal, find the force applied by each friend on the rope when the man is at a depth h .

Options

  1. Amg d^2 + 4h^2 4h
  2. Bmg d^2 + h^2 2h
  3. Cmg h d^2 + 4h^2
  4. Dmg d^2 + 4h^2 2h

Correct answer

A. mg d^2 + 4h^2 4h

Step-by-step solution

Let T be the force applied by each friend. Since the man is pulled up slowly, he is in equilibrium. The horizontal components of the tension forces balance each other, which implies the man is exactly in the middle of the ditch. Thus, the horizontal distance from the man to each pulley is d 2 . Let be the angle each rope makes with the vertical. From the geometry of the system, the length of the rope from the pulley to the man is given by: L = h^2 + ( d 2 )^2 = 4h^2 + d^2 2 The cosine of the angle is: = h L = 2h d^

Practice Newton's Laws of Motion on Quantrex Academy →

More from Newton's Laws of Motion

A block with a mass of 2 kg rests on a long frictionless horizontal table and is pulled horizontally by a constant force F . The block is observed to travel 10 m during the first tA block of mass 0.2 kg is suspended from the ceiling by a light string. A second block of mass 0.3 kg is suspended from the first block through another string. Determine the tensioPlaced on a smooth horizontal table, two blocks of equal mass m are connected by a light string. A constant force F is applied to pull one of the blocks along the line connecting tIn a TV picture tube, electrons are emitted from the cathode with negligible speed and attain a velocity of 5 10⁶ m/s after travelling one centimeter. Assuming straight line motionTravelling at 40 km/h , a car must be brought to a halt by applying brakes within the next 4.0 m . Given that the car weighs 2000 kg , determine the average force that must be applA particle of mass 50 g travels along a straight line. The variation of its speed with time is displayed in the figure. Determine the force acting on the particle at t = 2 , 4 , anTwo blocks A and B having masses m_A and m_B respectively are placed in contact on a frictionless table. An experimenter pushes block A from behind, causing the blocks to acceleratRaindrops, each having a radius of 1 mm and a mass of 4 mg , are falling at a speed of 30 m/s onto the head of a bald person. Upon splashing on the head, the drops come to rest. As Full Newton's Laws of Motion list All Concepts Of Physics MCQ Edition [Volume 1] PYQs