At 20∘c, the hole in an aluminum ring is 2.800 cm in diameter. you need to slip this ring over a steel shaft that has a room-temperature diameter of 2.804 cm . 1. to what common temperature should the ring and the shaft be heated so that the ring will just fit onto the shaft? coefficients of linear thermal expansion of steel and aluminum are 12×10−6 k−1 and23×10−6 k−1 respectively.

Explanation:

 To measure increase in length due to thermal expansion,  the formula is

L₂ =L₁ ( 1 + α t ) where L₁ length increases to L₁ due to rise in temperature by t.

L₂ in both the case is same so

for aluminium

L₂ = 2.8 ( 1 + 23 X 10⁻⁶ t )

for steel

L₂ = 2.804 ( 1 + 12 X 10⁻⁶ t )

2.8 ( 1 + .000023t) = 2.804 ( 1 + .000012 t )

Solving this equation

t = 122C

Final temperature of both = 122 +20 = 142 C

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

option number c is the right answer.