Question

Two discs having masses in the ratio 1:2 and radii in the ratio 1:8 roll down without slipping one by one from an inclined plane of height h. The ratio of their linear velocities on reaching the ground is????

Answer 1

The ratio of their speed will be 1:1

Explanation :

After reaching ground all the potential energy will be converted to kinetic energy,

For rolling object we know that the kinetic energy is given by,

KE = mv²/2 + Iω²/2

where I = moment of inertia = mr²/2

ω = angular velocity = v/r

Let the two disc have mass m & 2m and radii as r & 8r

For disc 1

PE = KE

=> mgh = mv²/2 + (1/2) x mr²/2 x (v/r)²

=> mgh = mv²/2 + mv²/4 = 3mv²/4

=> v = √(4gh/3)

similarly for disc 2, let the speed be v'

2mgh = 2mv'²/2 + (1/2) x (2m x 64r²/2) x (v'/64r²)

=> 2mgh = 3mv'²/2

=> v' = √(4gh/3)

Hence the ratio of their speed will be v:v' = 1:1

Answer 2

Answer:

Explanation:the velocity d

For object rolling without slipping is

V= square root of 2hgdivided by 1+ksquare divided by RSquare. So we should find v1:v2.

So mass m1=1

m2=2

R1=1

R2=8

h=h and the value of g=10

So by substituting the known values in the above equation we will get the answer as v1:v2=1:1