Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train, (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h, (c ) just after it is dropped from the window of a train accelerating with `1 m s^(-2)`, (d) lying on the floor of a train which is accelerating with `1 m s^(-2)` , the stone being at rest relative to the train. Neglect air resistance throughout.

Explanation

(a ) mass of stone m = 0 .1 kg g= 10 `ms^(-2)`
Magnitude of force `F= mg `
`=0.1 xx 10`
`=1 N`
this force will be in downward direction
(b ) When train moving with constant velocity of 36 kg `//` hr and stone is dropped from window of train
F= mg
`=0.1 xx 10`
When train is moving with constant
No other force will act except gravitational force (c )When train is travelling with acceleration of 1`ms^(-2) ` following force will act
Horizontal force `F_(1) = ma`
`=0.1 xx 1 =0.1 N`
Weight `F_(2) = mg`
`=0.1 xx 10`
`=1.N`
Resultant force
`F= squr(f_(1)^(2) + f_(2)^(2))`

`=squr (0.1)^(2) + (1)^(2))`
If resultant force make angle `theta ` with `F_(1)` then
tan `theta = (1)/( 0.1) = 10` (d ) When train is travelling at `1 ms^(2)` acceleration of stone lying in bottom of compartment of train will be `1ms^(2)` force acting on stone `=ma`
`=0.1 xx 1`
`=0.1 N`