Question

An inclined plane makes an angle of 30° with the horizontal electric field E of 100 V/m. A particle of mass 1 kg and charge 0.01 C slides down from a height of 1 m. If the coefficient of friction is 0.2, the time taken for the particle to reach the bottom is ______ sec.

 

Options

• 1.00

• 2.00

• 3.00

• 4.00

Answer 1

An inclined plane makes an angle of 30° with the horizontal electric field E of 100 V/m. A particle of mass 1 kg and charge 0.01 C slides down from a height of 1 m. If the coefficient of friction is 0.2, the time taken for the particle to reach the bottom is 2.00 sec.

Explanation:

f = μN

= μ(qE sin30° +  mg cos30°)

= `0.2(0.01 xx 100 xx 1/2 + 1 xx 10 xx 0.866)`

= 1.832 N

From the above figure,

`h/S  = sin30^circ`

S = `h/(sin 30^circ) = 1/(1/2)`

S = 2 m

Net downward force

F = mg sin30° - qE cos30° - f

= `(1 xx 10 xx 1/2 - 0.01 xx 100 xx 0.866 - 1.832)`

= 5 - 0.866 - 1.832

= 2.302 N

a = `f/m = 2.30/1 = 2.30` m/s²

S = ut + `1/2`at² (u = 0)

S = `1/2` at² 

t = `sqrt((2S)/a) = sqrt((2 xx 2)/2.30)`

t = 1.32 sec