Consider four round bodies of the same mass 9.8 kg and the same radius 0.42 m bu

Question

Consider four round bodies of the same mass
9.8 kg and the same radius 0.42 m but of dif-
ferent geometries – a solid sphere, a spherical
shell, a solid cylinder, and a cylindrical shell.
All four bodies start with zero initial veloc-
ity at the same distance from the bottom of
the incline and roll without slipping down the
same inclined plane.
Which body reaches the bottom first?
1. All four take the same time.
2. The cylindrical shell.
3. The solid cylinder.
4. Depends on the steepness of the incline.
5. The solid sphere.
6. The spherical shell.

Explanation / Answer

Moment of inertia of soild sphere I = ( 2/ 5) mr ^2 Moment of inertia of  spherical shell I = ( 2/3) mr ^ 2 Moment of inertia of  spherical shell I = ( 2/3) mr ^ 2 Moment of inertia of soild cylinder I =( 1/2) mr ^ 2 Moment of inertia of soild cylinder I =( 1/2) mr ^ 2 Moment of inertia of  cylindrical shell I= mr ^ 2 from law of conservation of angular momentum , Iw =constant i.e., low moment of inertia body have large angularspeed In above soild sphere have low moment of inertia.So, it havemaximum angular speed Therefore soild sphere reaches forst Moment of inertia of  cylindrical shell I= mr ^ 2 from law of conservation of angular momentum , Iw =constant i.e., low moment of inertia body have large angularspeed In above soild sphere have low moment of inertia.So, it havemaximum angular speed Therefore soild sphere reaches forst

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.