163765
The moment of inertia of two spheres of equal masses about their diameters are equal. If one of them is solid and other is hollow, the ratio of their radii is :
1 \(\sqrt{3}: \sqrt{5}\)
2 \(3: 5\)
3 \(\sqrt{5}: \sqrt{3}\)
4 \(5: 3\)
Explanation:
\(\sqrt{5}: \sqrt{3}\) Here \(\mathrm{I}_{\mathrm{s}}=\frac{2}{5} \mathrm{mR}_1^2\) and \(\mathrm{I}_{\mathrm{H}}=\frac{2}{3} \mathrm{mR}_2^2\) \(\therefore \frac{2}{5} \mathrm{mR}_1^2=\frac{2}{3} \mathrm{mR}_2^2\) or \(\frac{\mathrm{R}_1^2}{\mathrm{R}_2^2}=\frac{5}{3}\)
NCERT-XI- I -115
4 RBTS PAPER
163766
A thin uniform rod of length \(2 I\) is acted upon by a constant torque about an axis passsing through its CM and normal to it. The angular velocity changes from zero to \(\omega\) in time \(t\). the value of torque is :
163767
A uniform disc mass \(m\) and radius \(r\) is rotating with angular speed \(\omega\) in a horizontal plane about central axis. A particle of mass \(m\) is suddenly placed at the edge of the rim and sticks to it. The new angular speed is :
1 \(\frac{\omega}{\sqrt{3}}\)
2 \(\omega \sqrt{3}\)
3 \(\frac{\omega}{3}\)
4 \(3 \omega\)
Explanation:
Here \(\frac{1}{2} m r^2 \omega=\left(\frac{1}{2} m r^2+m r^2\right) \omega^{\prime}\) \(\therefore \omega^{\prime}=\frac{\omega}{3}\)
NCERT-XI- I -106
4 RBTS PAPER
163768
A mass is whirled in a circular path with constant angular velocity and its angular momentum is \(L\). If the string is now halved keeping the angular velocity same, the angular momentum is :
1 \(\frac{L}{4}\)
2 L
3 \(2 \mathrm{~L}\)
4 \(\frac{L}{2}\)
Explanation:
Here \(\quad L=m r^2 \omega\) and \(L^{\prime}=m\left(\frac{r}{2}\right)^2 . \omega=\frac{m r^2 \omega}{4}\) Thus \(\quad L^{\prime}=\frac{L}{4}\)
NCERT-XI- I -106
4 RBTS PAPER
163769
The M.I. of a body about a given axis is \(1.2 \mathrm{~kg} \mathrm{~m}\) and it is at rest. An angular acceleration of \(25 \mathrm{rad}\) \(\mathrm{s}^{-2}\) is applied to generate a K.E. of \(1500 \mathrm{~J}\) in the body. The duration for which acceleration is applied is
1 \(4 \mathrm{~s}\)
2 \(2 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
Explanation:
Here (K.E. \()_{\text {Rot. }}=\frac{1}{2} \mid \omega^2\) \( =\frac{1}{2} \times 1.2\left \) \( 1500 =0.6 \times 625 \times t^2 \) or \( \mathrm{t}^2=\frac{1500}{625 \times 0.6} \) \(\mathrm{t}^2=4\) or \(\mathrm{t}=2 \mathrm{~s}\)
163765
The moment of inertia of two spheres of equal masses about their diameters are equal. If one of them is solid and other is hollow, the ratio of their radii is :
1 \(\sqrt{3}: \sqrt{5}\)
2 \(3: 5\)
3 \(\sqrt{5}: \sqrt{3}\)
4 \(5: 3\)
Explanation:
\(\sqrt{5}: \sqrt{3}\) Here \(\mathrm{I}_{\mathrm{s}}=\frac{2}{5} \mathrm{mR}_1^2\) and \(\mathrm{I}_{\mathrm{H}}=\frac{2}{3} \mathrm{mR}_2^2\) \(\therefore \frac{2}{5} \mathrm{mR}_1^2=\frac{2}{3} \mathrm{mR}_2^2\) or \(\frac{\mathrm{R}_1^2}{\mathrm{R}_2^2}=\frac{5}{3}\)
NCERT-XI- I -115
4 RBTS PAPER
163766
A thin uniform rod of length \(2 I\) is acted upon by a constant torque about an axis passsing through its CM and normal to it. The angular velocity changes from zero to \(\omega\) in time \(t\). the value of torque is :
163767
A uniform disc mass \(m\) and radius \(r\) is rotating with angular speed \(\omega\) in a horizontal plane about central axis. A particle of mass \(m\) is suddenly placed at the edge of the rim and sticks to it. The new angular speed is :
1 \(\frac{\omega}{\sqrt{3}}\)
2 \(\omega \sqrt{3}\)
3 \(\frac{\omega}{3}\)
4 \(3 \omega\)
Explanation:
Here \(\frac{1}{2} m r^2 \omega=\left(\frac{1}{2} m r^2+m r^2\right) \omega^{\prime}\) \(\therefore \omega^{\prime}=\frac{\omega}{3}\)
NCERT-XI- I -106
4 RBTS PAPER
163768
A mass is whirled in a circular path with constant angular velocity and its angular momentum is \(L\). If the string is now halved keeping the angular velocity same, the angular momentum is :
1 \(\frac{L}{4}\)
2 L
3 \(2 \mathrm{~L}\)
4 \(\frac{L}{2}\)
Explanation:
Here \(\quad L=m r^2 \omega\) and \(L^{\prime}=m\left(\frac{r}{2}\right)^2 . \omega=\frac{m r^2 \omega}{4}\) Thus \(\quad L^{\prime}=\frac{L}{4}\)
NCERT-XI- I -106
4 RBTS PAPER
163769
The M.I. of a body about a given axis is \(1.2 \mathrm{~kg} \mathrm{~m}\) and it is at rest. An angular acceleration of \(25 \mathrm{rad}\) \(\mathrm{s}^{-2}\) is applied to generate a K.E. of \(1500 \mathrm{~J}\) in the body. The duration for which acceleration is applied is
1 \(4 \mathrm{~s}\)
2 \(2 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
Explanation:
Here (K.E. \()_{\text {Rot. }}=\frac{1}{2} \mid \omega^2\) \( =\frac{1}{2} \times 1.2\left \) \( 1500 =0.6 \times 625 \times t^2 \) or \( \mathrm{t}^2=\frac{1500}{625 \times 0.6} \) \(\mathrm{t}^2=4\) or \(\mathrm{t}=2 \mathrm{~s}\)
163765
The moment of inertia of two spheres of equal masses about their diameters are equal. If one of them is solid and other is hollow, the ratio of their radii is :
1 \(\sqrt{3}: \sqrt{5}\)
2 \(3: 5\)
3 \(\sqrt{5}: \sqrt{3}\)
4 \(5: 3\)
Explanation:
\(\sqrt{5}: \sqrt{3}\) Here \(\mathrm{I}_{\mathrm{s}}=\frac{2}{5} \mathrm{mR}_1^2\) and \(\mathrm{I}_{\mathrm{H}}=\frac{2}{3} \mathrm{mR}_2^2\) \(\therefore \frac{2}{5} \mathrm{mR}_1^2=\frac{2}{3} \mathrm{mR}_2^2\) or \(\frac{\mathrm{R}_1^2}{\mathrm{R}_2^2}=\frac{5}{3}\)
NCERT-XI- I -115
4 RBTS PAPER
163766
A thin uniform rod of length \(2 I\) is acted upon by a constant torque about an axis passsing through its CM and normal to it. The angular velocity changes from zero to \(\omega\) in time \(t\). the value of torque is :
163767
A uniform disc mass \(m\) and radius \(r\) is rotating with angular speed \(\omega\) in a horizontal plane about central axis. A particle of mass \(m\) is suddenly placed at the edge of the rim and sticks to it. The new angular speed is :
1 \(\frac{\omega}{\sqrt{3}}\)
2 \(\omega \sqrt{3}\)
3 \(\frac{\omega}{3}\)
4 \(3 \omega\)
Explanation:
Here \(\frac{1}{2} m r^2 \omega=\left(\frac{1}{2} m r^2+m r^2\right) \omega^{\prime}\) \(\therefore \omega^{\prime}=\frac{\omega}{3}\)
NCERT-XI- I -106
4 RBTS PAPER
163768
A mass is whirled in a circular path with constant angular velocity and its angular momentum is \(L\). If the string is now halved keeping the angular velocity same, the angular momentum is :
1 \(\frac{L}{4}\)
2 L
3 \(2 \mathrm{~L}\)
4 \(\frac{L}{2}\)
Explanation:
Here \(\quad L=m r^2 \omega\) and \(L^{\prime}=m\left(\frac{r}{2}\right)^2 . \omega=\frac{m r^2 \omega}{4}\) Thus \(\quad L^{\prime}=\frac{L}{4}\)
NCERT-XI- I -106
4 RBTS PAPER
163769
The M.I. of a body about a given axis is \(1.2 \mathrm{~kg} \mathrm{~m}\) and it is at rest. An angular acceleration of \(25 \mathrm{rad}\) \(\mathrm{s}^{-2}\) is applied to generate a K.E. of \(1500 \mathrm{~J}\) in the body. The duration for which acceleration is applied is
1 \(4 \mathrm{~s}\)
2 \(2 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
Explanation:
Here (K.E. \()_{\text {Rot. }}=\frac{1}{2} \mid \omega^2\) \( =\frac{1}{2} \times 1.2\left \) \( 1500 =0.6 \times 625 \times t^2 \) or \( \mathrm{t}^2=\frac{1500}{625 \times 0.6} \) \(\mathrm{t}^2=4\) or \(\mathrm{t}=2 \mathrm{~s}\)
NEET Test Series from KOTA - 10 Papers In MS WORD
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4 RBTS PAPER
163765
The moment of inertia of two spheres of equal masses about their diameters are equal. If one of them is solid and other is hollow, the ratio of their radii is :
1 \(\sqrt{3}: \sqrt{5}\)
2 \(3: 5\)
3 \(\sqrt{5}: \sqrt{3}\)
4 \(5: 3\)
Explanation:
\(\sqrt{5}: \sqrt{3}\) Here \(\mathrm{I}_{\mathrm{s}}=\frac{2}{5} \mathrm{mR}_1^2\) and \(\mathrm{I}_{\mathrm{H}}=\frac{2}{3} \mathrm{mR}_2^2\) \(\therefore \frac{2}{5} \mathrm{mR}_1^2=\frac{2}{3} \mathrm{mR}_2^2\) or \(\frac{\mathrm{R}_1^2}{\mathrm{R}_2^2}=\frac{5}{3}\)
NCERT-XI- I -115
4 RBTS PAPER
163766
A thin uniform rod of length \(2 I\) is acted upon by a constant torque about an axis passsing through its CM and normal to it. The angular velocity changes from zero to \(\omega\) in time \(t\). the value of torque is :
163767
A uniform disc mass \(m\) and radius \(r\) is rotating with angular speed \(\omega\) in a horizontal plane about central axis. A particle of mass \(m\) is suddenly placed at the edge of the rim and sticks to it. The new angular speed is :
1 \(\frac{\omega}{\sqrt{3}}\)
2 \(\omega \sqrt{3}\)
3 \(\frac{\omega}{3}\)
4 \(3 \omega\)
Explanation:
Here \(\frac{1}{2} m r^2 \omega=\left(\frac{1}{2} m r^2+m r^2\right) \omega^{\prime}\) \(\therefore \omega^{\prime}=\frac{\omega}{3}\)
NCERT-XI- I -106
4 RBTS PAPER
163768
A mass is whirled in a circular path with constant angular velocity and its angular momentum is \(L\). If the string is now halved keeping the angular velocity same, the angular momentum is :
1 \(\frac{L}{4}\)
2 L
3 \(2 \mathrm{~L}\)
4 \(\frac{L}{2}\)
Explanation:
Here \(\quad L=m r^2 \omega\) and \(L^{\prime}=m\left(\frac{r}{2}\right)^2 . \omega=\frac{m r^2 \omega}{4}\) Thus \(\quad L^{\prime}=\frac{L}{4}\)
NCERT-XI- I -106
4 RBTS PAPER
163769
The M.I. of a body about a given axis is \(1.2 \mathrm{~kg} \mathrm{~m}\) and it is at rest. An angular acceleration of \(25 \mathrm{rad}\) \(\mathrm{s}^{-2}\) is applied to generate a K.E. of \(1500 \mathrm{~J}\) in the body. The duration for which acceleration is applied is
1 \(4 \mathrm{~s}\)
2 \(2 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
Explanation:
Here (K.E. \()_{\text {Rot. }}=\frac{1}{2} \mid \omega^2\) \( =\frac{1}{2} \times 1.2\left \) \( 1500 =0.6 \times 625 \times t^2 \) or \( \mathrm{t}^2=\frac{1500}{625 \times 0.6} \) \(\mathrm{t}^2=4\) or \(\mathrm{t}=2 \mathrm{~s}\)
163765
The moment of inertia of two spheres of equal masses about their diameters are equal. If one of them is solid and other is hollow, the ratio of their radii is :
1 \(\sqrt{3}: \sqrt{5}\)
2 \(3: 5\)
3 \(\sqrt{5}: \sqrt{3}\)
4 \(5: 3\)
Explanation:
\(\sqrt{5}: \sqrt{3}\) Here \(\mathrm{I}_{\mathrm{s}}=\frac{2}{5} \mathrm{mR}_1^2\) and \(\mathrm{I}_{\mathrm{H}}=\frac{2}{3} \mathrm{mR}_2^2\) \(\therefore \frac{2}{5} \mathrm{mR}_1^2=\frac{2}{3} \mathrm{mR}_2^2\) or \(\frac{\mathrm{R}_1^2}{\mathrm{R}_2^2}=\frac{5}{3}\)
NCERT-XI- I -115
4 RBTS PAPER
163766
A thin uniform rod of length \(2 I\) is acted upon by a constant torque about an axis passsing through its CM and normal to it. The angular velocity changes from zero to \(\omega\) in time \(t\). the value of torque is :
163767
A uniform disc mass \(m\) and radius \(r\) is rotating with angular speed \(\omega\) in a horizontal plane about central axis. A particle of mass \(m\) is suddenly placed at the edge of the rim and sticks to it. The new angular speed is :
1 \(\frac{\omega}{\sqrt{3}}\)
2 \(\omega \sqrt{3}\)
3 \(\frac{\omega}{3}\)
4 \(3 \omega\)
Explanation:
Here \(\frac{1}{2} m r^2 \omega=\left(\frac{1}{2} m r^2+m r^2\right) \omega^{\prime}\) \(\therefore \omega^{\prime}=\frac{\omega}{3}\)
NCERT-XI- I -106
4 RBTS PAPER
163768
A mass is whirled in a circular path with constant angular velocity and its angular momentum is \(L\). If the string is now halved keeping the angular velocity same, the angular momentum is :
1 \(\frac{L}{4}\)
2 L
3 \(2 \mathrm{~L}\)
4 \(\frac{L}{2}\)
Explanation:
Here \(\quad L=m r^2 \omega\) and \(L^{\prime}=m\left(\frac{r}{2}\right)^2 . \omega=\frac{m r^2 \omega}{4}\) Thus \(\quad L^{\prime}=\frac{L}{4}\)
NCERT-XI- I -106
4 RBTS PAPER
163769
The M.I. of a body about a given axis is \(1.2 \mathrm{~kg} \mathrm{~m}\) and it is at rest. An angular acceleration of \(25 \mathrm{rad}\) \(\mathrm{s}^{-2}\) is applied to generate a K.E. of \(1500 \mathrm{~J}\) in the body. The duration for which acceleration is applied is
1 \(4 \mathrm{~s}\)
2 \(2 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
Explanation:
Here (K.E. \()_{\text {Rot. }}=\frac{1}{2} \mid \omega^2\) \( =\frac{1}{2} \times 1.2\left \) \( 1500 =0.6 \times 625 \times t^2 \) or \( \mathrm{t}^2=\frac{1500}{625 \times 0.6} \) \(\mathrm{t}^2=4\) or \(\mathrm{t}=2 \mathrm{~s}\)