269465
A uniform circular disc of radius \(R\) is rotating about its own axis with moment of inertia \(I\) at an angular velocity \(\omega\) If a denser particle of mass \(m\) is gently attached to the rim of disc than its angular velocity is
269466
A particle of mass\(m\) is rotating along a circular path of radius \(r\). Its angular momentum is \(L\). The centripetal force acting on the particle is
1 \(\frac{L^{2}}{m r}\)
2 \(\frac{L^{2} m}{r}\)
3 \(\frac{L^{2}}{m r^{2}}\)
4 \(\frac{L^{2}}{m r^{3}}\)
Explanation:
\(L=m v r \Rightarrow v=\frac{L}{m r}\)
centripetal force \(F=\frac{m v^{2}}{r}=\frac{L^{2}}{m r^{3}}\)
Rotational Motion
269467
\(\vec{F}=a \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k}\). The value of ' \(a\) ' for which the angular momentum is conserved is
1 -1
2 0
3 1
4 2
Explanation:
\(\vec{\tau}=\vec{r} \times \vec{F}\) and \(\tau=\frac{d L}{d t}=0\)
Rotational Motion
269468
If earth shrinks to\(1 / 64\) of its volume with mass remaining same, duration of the day will be
1 \(1.5 \mathrm{~h}\)
2 \(3 h\)
3 \(4.5 \mathrm{~h}\)
4 \(6 \mathrm{~h}\)
Explanation:
\(I \omega=\frac{2}{5} M R^{2} \omega=\) constant and \(V \propto R^{3}\)
269465
A uniform circular disc of radius \(R\) is rotating about its own axis with moment of inertia \(I\) at an angular velocity \(\omega\) If a denser particle of mass \(m\) is gently attached to the rim of disc than its angular velocity is
269466
A particle of mass\(m\) is rotating along a circular path of radius \(r\). Its angular momentum is \(L\). The centripetal force acting on the particle is
1 \(\frac{L^{2}}{m r}\)
2 \(\frac{L^{2} m}{r}\)
3 \(\frac{L^{2}}{m r^{2}}\)
4 \(\frac{L^{2}}{m r^{3}}\)
Explanation:
\(L=m v r \Rightarrow v=\frac{L}{m r}\)
centripetal force \(F=\frac{m v^{2}}{r}=\frac{L^{2}}{m r^{3}}\)
Rotational Motion
269467
\(\vec{F}=a \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k}\). The value of ' \(a\) ' for which the angular momentum is conserved is
1 -1
2 0
3 1
4 2
Explanation:
\(\vec{\tau}=\vec{r} \times \vec{F}\) and \(\tau=\frac{d L}{d t}=0\)
Rotational Motion
269468
If earth shrinks to\(1 / 64\) of its volume with mass remaining same, duration of the day will be
1 \(1.5 \mathrm{~h}\)
2 \(3 h\)
3 \(4.5 \mathrm{~h}\)
4 \(6 \mathrm{~h}\)
Explanation:
\(I \omega=\frac{2}{5} M R^{2} \omega=\) constant and \(V \propto R^{3}\)
269465
A uniform circular disc of radius \(R\) is rotating about its own axis with moment of inertia \(I\) at an angular velocity \(\omega\) If a denser particle of mass \(m\) is gently attached to the rim of disc than its angular velocity is
269466
A particle of mass\(m\) is rotating along a circular path of radius \(r\). Its angular momentum is \(L\). The centripetal force acting on the particle is
1 \(\frac{L^{2}}{m r}\)
2 \(\frac{L^{2} m}{r}\)
3 \(\frac{L^{2}}{m r^{2}}\)
4 \(\frac{L^{2}}{m r^{3}}\)
Explanation:
\(L=m v r \Rightarrow v=\frac{L}{m r}\)
centripetal force \(F=\frac{m v^{2}}{r}=\frac{L^{2}}{m r^{3}}\)
Rotational Motion
269467
\(\vec{F}=a \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k}\). The value of ' \(a\) ' for which the angular momentum is conserved is
1 -1
2 0
3 1
4 2
Explanation:
\(\vec{\tau}=\vec{r} \times \vec{F}\) and \(\tau=\frac{d L}{d t}=0\)
Rotational Motion
269468
If earth shrinks to\(1 / 64\) of its volume with mass remaining same, duration of the day will be
1 \(1.5 \mathrm{~h}\)
2 \(3 h\)
3 \(4.5 \mathrm{~h}\)
4 \(6 \mathrm{~h}\)
Explanation:
\(I \omega=\frac{2}{5} M R^{2} \omega=\) constant and \(V \propto R^{3}\)
269465
A uniform circular disc of radius \(R\) is rotating about its own axis with moment of inertia \(I\) at an angular velocity \(\omega\) If a denser particle of mass \(m\) is gently attached to the rim of disc than its angular velocity is
269466
A particle of mass\(m\) is rotating along a circular path of radius \(r\). Its angular momentum is \(L\). The centripetal force acting on the particle is
1 \(\frac{L^{2}}{m r}\)
2 \(\frac{L^{2} m}{r}\)
3 \(\frac{L^{2}}{m r^{2}}\)
4 \(\frac{L^{2}}{m r^{3}}\)
Explanation:
\(L=m v r \Rightarrow v=\frac{L}{m r}\)
centripetal force \(F=\frac{m v^{2}}{r}=\frac{L^{2}}{m r^{3}}\)
Rotational Motion
269467
\(\vec{F}=a \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\vec{r}=2 \hat{i}-6 \hat{j}-12 \hat{k}\). The value of ' \(a\) ' for which the angular momentum is conserved is
1 -1
2 0
3 1
4 2
Explanation:
\(\vec{\tau}=\vec{r} \times \vec{F}\) and \(\tau=\frac{d L}{d t}=0\)
Rotational Motion
269468
If earth shrinks to\(1 / 64\) of its volume with mass remaining same, duration of the day will be
1 \(1.5 \mathrm{~h}\)
2 \(3 h\)
3 \(4.5 \mathrm{~h}\)
4 \(6 \mathrm{~h}\)
Explanation:
\(I \omega=\frac{2}{5} M R^{2} \omega=\) constant and \(V \propto R^{3}\)
