A force on an object of mass 100 g is ( 10î + 5ĵ ) N. The position of that object at t = 2 s is ( aî + bĵ ) m after starting from rest. The value of a/b will be ___________.

Solution

Physics sir · 3 steps

A constant force from rest means each displacement component follows the force component.

1. Find acceleration. Convert the mass to 0.1 kg and use a⃗ = F⃗/m. This gives a⃗ = (100î + 50ĵ) m s⁻², which is constant.

   r⃗ = 1/2a⃗ t²

2. Put in numbers. The object starts from rest at the origin, so at t = 2 s, a = 1/2 × 100 × 4 = 200 m and b = 1/2 × 50 × 4 = 100 m.
3. So. a/b = 200/100 = 2, which is the same as Fₓ/F_y = 10/5.

The common slip: 0.5. Taking the ratio upside down as b/a gives 0.5. The question asks for the î component over the ĵ component.

The idea to keep. From rest under a constant force, the displacement points along the force. So the ratio of displacement components equals the ratio of force components. Mass and time cancel out.

Answer from the NTA final answer key. Solution by PrepWiser.