05. Rotational Motion and Rotational Energy
Rotational Motion

150321 A flywheel of mass \(2 \mathrm{~kg}\) has radius of gyration \(0.5 \mathrm{~m}\). If it makes 10 r.p.s. then its rotational kinetic energy will be

1 \(100 \pi^{2}\) erg
2 \(50 \pi^{2} \mathrm{~J}\)
3 \(100 \pi^{2} \mathrm{~J}\)
4 \(50 \pi^{2}\) erg
Rotational Motion

150322 A ring and disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is \(4 \mathrm{~J}\) then total kinetic energy of the disc is

1 \(3 \mathrm{~J}\)
2 \(8 \mathrm{~J}\)
3 \(6 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
\(\left[\begin{array}{l}\mathrm{I}=\mathrm{mk}^{2} \\ \omega=2 \pi \mathrm{f}\end{array}\right]\)
Rotational Motion

150323 A solid sphere of radius \(r\) is rolling without sliding. The ratio of rotational kinetic energy and total kinetic energy associated with the sphere is

1 \(\frac{1}{5}\)
2 \(\frac{2}{5}\)
3 \(\frac{1}{2}\)
4 \(\frac{2}{7}\)
Rotational Motion

150324 A hollow sphere rolls down from the top of inclined plane. Its velocity on reaching the bottom of plane is \(V_{1}\). When the same sphere slides down from the top of the plane, its velocity on reaching the bottom is \(V_{2}\). The ratio \(V_{2}: V_{1}\) is [Take M.I. of hollow sphere \(=\) \(\frac{2}{3} \mathrm{MR}^{2}\) ]

1 \(\sqrt{\frac{5}{3}}\)
2 \(\sqrt{\frac{7}{5}}\)
3 \(\sqrt{\frac{3}{5}}\)
4 \(\sqrt{\frac{5}{7}}\)
Rotational Motion

150321 A flywheel of mass \(2 \mathrm{~kg}\) has radius of gyration \(0.5 \mathrm{~m}\). If it makes 10 r.p.s. then its rotational kinetic energy will be

1 \(100 \pi^{2}\) erg
2 \(50 \pi^{2} \mathrm{~J}\)
3 \(100 \pi^{2} \mathrm{~J}\)
4 \(50 \pi^{2}\) erg
Rotational Motion

150322 A ring and disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is \(4 \mathrm{~J}\) then total kinetic energy of the disc is

1 \(3 \mathrm{~J}\)
2 \(8 \mathrm{~J}\)
3 \(6 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
\(\left[\begin{array}{l}\mathrm{I}=\mathrm{mk}^{2} \\ \omega=2 \pi \mathrm{f}\end{array}\right]\)
Rotational Motion

150323 A solid sphere of radius \(r\) is rolling without sliding. The ratio of rotational kinetic energy and total kinetic energy associated with the sphere is

1 \(\frac{1}{5}\)
2 \(\frac{2}{5}\)
3 \(\frac{1}{2}\)
4 \(\frac{2}{7}\)
Rotational Motion

150324 A hollow sphere rolls down from the top of inclined plane. Its velocity on reaching the bottom of plane is \(V_{1}\). When the same sphere slides down from the top of the plane, its velocity on reaching the bottom is \(V_{2}\). The ratio \(V_{2}: V_{1}\) is [Take M.I. of hollow sphere \(=\) \(\frac{2}{3} \mathrm{MR}^{2}\) ]

1 \(\sqrt{\frac{5}{3}}\)
2 \(\sqrt{\frac{7}{5}}\)
3 \(\sqrt{\frac{3}{5}}\)
4 \(\sqrt{\frac{5}{7}}\)
Rotational Motion

150321 A flywheel of mass \(2 \mathrm{~kg}\) has radius of gyration \(0.5 \mathrm{~m}\). If it makes 10 r.p.s. then its rotational kinetic energy will be

1 \(100 \pi^{2}\) erg
2 \(50 \pi^{2} \mathrm{~J}\)
3 \(100 \pi^{2} \mathrm{~J}\)
4 \(50 \pi^{2}\) erg
Rotational Motion

150322 A ring and disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is \(4 \mathrm{~J}\) then total kinetic energy of the disc is

1 \(3 \mathrm{~J}\)
2 \(8 \mathrm{~J}\)
3 \(6 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
\(\left[\begin{array}{l}\mathrm{I}=\mathrm{mk}^{2} \\ \omega=2 \pi \mathrm{f}\end{array}\right]\)
Rotational Motion

150323 A solid sphere of radius \(r\) is rolling without sliding. The ratio of rotational kinetic energy and total kinetic energy associated with the sphere is

1 \(\frac{1}{5}\)
2 \(\frac{2}{5}\)
3 \(\frac{1}{2}\)
4 \(\frac{2}{7}\)
Rotational Motion

150324 A hollow sphere rolls down from the top of inclined plane. Its velocity on reaching the bottom of plane is \(V_{1}\). When the same sphere slides down from the top of the plane, its velocity on reaching the bottom is \(V_{2}\). The ratio \(V_{2}: V_{1}\) is [Take M.I. of hollow sphere \(=\) \(\frac{2}{3} \mathrm{MR}^{2}\) ]

1 \(\sqrt{\frac{5}{3}}\)
2 \(\sqrt{\frac{7}{5}}\)
3 \(\sqrt{\frac{3}{5}}\)
4 \(\sqrt{\frac{5}{7}}\)
Rotational Motion

150321 A flywheel of mass \(2 \mathrm{~kg}\) has radius of gyration \(0.5 \mathrm{~m}\). If it makes 10 r.p.s. then its rotational kinetic energy will be

1 \(100 \pi^{2}\) erg
2 \(50 \pi^{2} \mathrm{~J}\)
3 \(100 \pi^{2} \mathrm{~J}\)
4 \(50 \pi^{2}\) erg
Rotational Motion

150322 A ring and disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is \(4 \mathrm{~J}\) then total kinetic energy of the disc is

1 \(3 \mathrm{~J}\)
2 \(8 \mathrm{~J}\)
3 \(6 \mathrm{~J}\)
4 \(2 \mathrm{~J}\)
\(\left[\begin{array}{l}\mathrm{I}=\mathrm{mk}^{2} \\ \omega=2 \pi \mathrm{f}\end{array}\right]\)
Rotational Motion

150323 A solid sphere of radius \(r\) is rolling without sliding. The ratio of rotational kinetic energy and total kinetic energy associated with the sphere is

1 \(\frac{1}{5}\)
2 \(\frac{2}{5}\)
3 \(\frac{1}{2}\)
4 \(\frac{2}{7}\)
Rotational Motion

150324 A hollow sphere rolls down from the top of inclined plane. Its velocity on reaching the bottom of plane is \(V_{1}\). When the same sphere slides down from the top of the plane, its velocity on reaching the bottom is \(V_{2}\). The ratio \(V_{2}: V_{1}\) is [Take M.I. of hollow sphere \(=\) \(\frac{2}{3} \mathrm{MR}^{2}\) ]

1 \(\sqrt{\frac{5}{3}}\)
2 \(\sqrt{\frac{7}{5}}\)
3 \(\sqrt{\frac{3}{5}}\)
4 \(\sqrt{\frac{5}{7}}\)