constrain motion and newton second law in constrain motion questions with solutions

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• Multi-correctdifficultNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  Two equal masses A and B are connected by a massless string over the pulley arrangement shown and released from rest. Which statements are correct?

  

  Select all that apply

  • Option A

    T=mg/2

  • Option B

    T=mg/4

  • Option C

    aₐ=g/2

  • Option D

    aₐ=3g/4

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• MCQmediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  A vertical rod slides down with acceleration a while remaining in contact with a wedge that accelerates horizontally. If the wedge angle is θ, the wedge acceleration is:

  

  Options

  • Option A

    a secθ

  • Option B

    a cosecθ

  • Option C

    a tanθ

  • Option D

    a cotθ

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• NumericdifficultNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  In the multi-pulley arrangement shown, the indicated velocities are A upward 8 m s⁻¹, B downward 2 m s⁻¹, C upward 2 m s⁻¹, D downward 1 m s⁻¹ and the free end F moves right at 4 m s⁻¹. Find the speed of block E in m s⁻¹.

  

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• MCQmediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  Two blocks A and B move horizontally with speeds v₁ and v₂ while connected to a fixed pulley by strings making angles θ₁ and θ₂ with the horizontal. The ratio v₁/v₂ is:

  

  Options

  • Option A

    cosθ₁/cosθ₂

  • Option B

    cosθ₂/cosθ₁

  • Option C

    sinθ₁/sinθ₂

  • Option D

    sinθ₂/sinθ₁

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• NumericdifficultNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  In the pulley system shown, cable ends A and B each move outward with speed 2 m s⁻¹. Find the upward velocity of the load m in m s⁻¹.

  

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• MCQmediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  In the pulley arrangement shown all surfaces are smooth. m₁=20 kg, m₂=30 kg and F=180 N. The accelerations are:

  

  Options

  • Option A

    a₁=9 m s⁻², a₂=0

  • Option B

    a₁=9 m s⁻², a₂=9 m s⁻²

  • Option C

    a₁=0, a₂=9 m s⁻²

  • Option D

    None

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• IntegermediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  In the pulley arrangement shown, mass A is four times mass B. At one instant B is released while the system is already moving; A falls through h=20 cm before hitting the ground. Take g=10 m s⁻². Find the maximum additional height, in cm, reached by B above its initial position.

  

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• MCQmediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  Block B moves to the right at 300 mm s⁻¹ in the pulley arrangement shown. The velocity of block A is:

  

  Options

  • Option A

    200 mm s⁻¹

  • Option B

    100 mm s⁻¹

  • Option C

    450 mm s⁻¹

  • Option D

    150 mm s⁻¹

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• MCQmediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  A 10 kg monkey holds a rope passing over a fixed pulley; a 5 kg mass hangs on the other side. If the monkey exerts 80 N on the rope, its acceleration relative to the rope is:

  

  Options

  • Option A

    2 m s⁻² downward

  • Option B

    4 m s⁻² upward

  • Option C

    4 m s⁻² downward

  • Option D

    8 m s⁻² downward

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• MCQmediumNewtons law of motion and Frictionconstrain motion and newton second law in constrain motion

  At an instant the top pulley moves upward at 1 m s⁻¹, block A moves right at 3.25 m s⁻¹ and block B moves right at √3 m s⁻¹; the right string makes 30° with the horizontal. Find θ as shown.

  

  Options

  • Option A

    tan⁻¹($\frac{3}{4}$)

  • Option B

    tan⁻¹(4/3)

  • Option C

    tan⁻¹(3/8)

  • Option D

    None

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