A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance at the same time. If the angle of the plane down which the sphere rolls is 30° . The angle of the other plane is

Question

A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance at the same time. If the angle of the plane down which the sphere rolls is 30° . The angle of the other plane is (A) 60°  (B) 53°  (C) 37°  (D) 45°

Tardigrade Admin · Accepted Answer

If radius of gyration is K , For sphere, K12=(2/5)R2, θ 1=30° , For hollow cylinder, K22=R2, θ 2=? (1 + (2/5)/sin 30 ° )=(1 + 1/sin â¡ θ 2) sin θ 2=(5/7)=0.7143 θ =45°

Q. A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance at the same time. If the angle of the plane down which the sphere rolls is $3 0^{\circ}$ . The angle of the other plane is

$6 0^{\circ}$

$5 3^{\circ}$

$3 7^{\circ}$

$4 5^{\circ}$

If radius of gyration is $K$ ,
For sphere, $K_{1}^{2} = \frac{2}{5} R^{2}, θ_{1} = 3 0^{\circ}$ ,
For hollow cylinder, $K_{2}^{2} = R^{2}, θ_{2} = ?$
$\frac{1 + \frac{2}{5}}{s in 3 0 ^{\circ}} = \frac{1 + 1}{s in θ _{2}}$
$s in θ_{2} = \frac{5}{7} = 0.7143$
$θ = 4 5^{\circ}$

Q. A sphere and a hollow cylinder roll without slipping down two separate inclined planes and travel the same distance at the same time. If the angle of the plane down which the sphere rolls is 30∘ . The angle of the other plane is

60∘

53∘

37∘

45∘