149961
A solid sphere of radius \(R\) makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle \(\theta\). If the radius of gyration is \(\mathbf{k}\), then its acceleration is
149963
The minimum and maximum distance of planet from sun is \(r_{\text {min }}\) and \(r_{\text {max }}\). If velocity at \(r_{\text {max }}\) is \(V_{0}\) then find velocity at \(r_{\text {min }}\).
A By law of conservation angular momentum, \(\mathrm{mV}_{0} \mathrm{r}_{\max }=\mathrm{mVr}_{\text {min }}\) \(\mathrm{V}=\frac{\mathrm{V}_{0} \mathrm{r}_{\max }}{\mathrm{r}_{\min }}\) By Kepler's law the areal velocity \(=\frac{\mathrm{L}}{2 \mathrm{~m}}\) (constant) Hence, L (angular momentum) is constant.
AIIMS-26.05.2018(E)
Rotational Motion
149964
A Light rope is wound around a hollow cylinder of mass \(4 \mathrm{~kg}\) and radius \(40 \mathrm{~cm}\). If the rope is pulled with a force of \(40 \mathrm{~N}\), its angular acceleration is
149961
A solid sphere of radius \(R\) makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle \(\theta\). If the radius of gyration is \(\mathbf{k}\), then its acceleration is
149963
The minimum and maximum distance of planet from sun is \(r_{\text {min }}\) and \(r_{\text {max }}\). If velocity at \(r_{\text {max }}\) is \(V_{0}\) then find velocity at \(r_{\text {min }}\).
A By law of conservation angular momentum, \(\mathrm{mV}_{0} \mathrm{r}_{\max }=\mathrm{mVr}_{\text {min }}\) \(\mathrm{V}=\frac{\mathrm{V}_{0} \mathrm{r}_{\max }}{\mathrm{r}_{\min }}\) By Kepler's law the areal velocity \(=\frac{\mathrm{L}}{2 \mathrm{~m}}\) (constant) Hence, L (angular momentum) is constant.
AIIMS-26.05.2018(E)
Rotational Motion
149964
A Light rope is wound around a hollow cylinder of mass \(4 \mathrm{~kg}\) and radius \(40 \mathrm{~cm}\). If the rope is pulled with a force of \(40 \mathrm{~N}\), its angular acceleration is
149961
A solid sphere of radius \(R\) makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle \(\theta\). If the radius of gyration is \(\mathbf{k}\), then its acceleration is
149963
The minimum and maximum distance of planet from sun is \(r_{\text {min }}\) and \(r_{\text {max }}\). If velocity at \(r_{\text {max }}\) is \(V_{0}\) then find velocity at \(r_{\text {min }}\).
A By law of conservation angular momentum, \(\mathrm{mV}_{0} \mathrm{r}_{\max }=\mathrm{mVr}_{\text {min }}\) \(\mathrm{V}=\frac{\mathrm{V}_{0} \mathrm{r}_{\max }}{\mathrm{r}_{\min }}\) By Kepler's law the areal velocity \(=\frac{\mathrm{L}}{2 \mathrm{~m}}\) (constant) Hence, L (angular momentum) is constant.
AIIMS-26.05.2018(E)
Rotational Motion
149964
A Light rope is wound around a hollow cylinder of mass \(4 \mathrm{~kg}\) and radius \(40 \mathrm{~cm}\). If the rope is pulled with a force of \(40 \mathrm{~N}\), its angular acceleration is
149961
A solid sphere of radius \(R\) makes a perfect rolling down on a plane which is inclined to the horizontal axis at an angle \(\theta\). If the radius of gyration is \(\mathbf{k}\), then its acceleration is
149963
The minimum and maximum distance of planet from sun is \(r_{\text {min }}\) and \(r_{\text {max }}\). If velocity at \(r_{\text {max }}\) is \(V_{0}\) then find velocity at \(r_{\text {min }}\).
A By law of conservation angular momentum, \(\mathrm{mV}_{0} \mathrm{r}_{\max }=\mathrm{mVr}_{\text {min }}\) \(\mathrm{V}=\frac{\mathrm{V}_{0} \mathrm{r}_{\max }}{\mathrm{r}_{\min }}\) By Kepler's law the areal velocity \(=\frac{\mathrm{L}}{2 \mathrm{~m}}\) (constant) Hence, L (angular momentum) is constant.
AIIMS-26.05.2018(E)
Rotational Motion
149964
A Light rope is wound around a hollow cylinder of mass \(4 \mathrm{~kg}\) and radius \(40 \mathrm{~cm}\). If the rope is pulled with a force of \(40 \mathrm{~N}\), its angular acceleration is
