266605
A flat horizontal board moves up and down in SHM of amplitude a. Then the shortest permisible time period of the vibration such that an object placed on the board may not loose contact with the board is:
1 \(2 \pi \sqrt{\frac{g}{a}}\)
2 \(2 \pi \sqrt{\frac{a}{g}}\)
3 \(2 \pi \sqrt{g \times a}\)
4 \(\frac{1}{2 \pi} \sqrt{\frac{g}{a}}\)
Explanation:
b \(m a \omega^2=m g\) ㅇ \(\omega=\sqrt{\frac{g}{a}}\) or \(\frac{2 \pi}{T}=\sqrt{\frac{g}{a}}\) or \(T=2 \pi \sqrt{\frac{a}{g}}\)
TEST SERIES (PHYSICS FST)
266607
From a uniform disc of radius \(R\), a circular section of radius R \(/ 2\) is cut out. The centre of hole is a R/2 from the centre of the original disc. moment of inertia of resulting body about \(O_1\).
b \[ \begin{aligned} I_1 & =\frac{1}{2} M R^2+M\left(\frac{R}{2}\right)^2 \\ & =\frac{3}{4} M R^2 \end{aligned} \] \(\mathrm{I}_2=\frac{1}{2} \frac{M}{4}\left(\frac{\mathrm{R}}{2}\right)^2=\frac{1}{32} M \mathrm{R}^2\) Moment of inetia along point \(\mathrm{O}_1\) \(\mathrm{I}_1-\mathrm{I}_2\) \(=\frac{23}{32} \mathrm{MR}^2\)
266605
A flat horizontal board moves up and down in SHM of amplitude a. Then the shortest permisible time period of the vibration such that an object placed on the board may not loose contact with the board is:
1 \(2 \pi \sqrt{\frac{g}{a}}\)
2 \(2 \pi \sqrt{\frac{a}{g}}\)
3 \(2 \pi \sqrt{g \times a}\)
4 \(\frac{1}{2 \pi} \sqrt{\frac{g}{a}}\)
Explanation:
b \(m a \omega^2=m g\) ㅇ \(\omega=\sqrt{\frac{g}{a}}\) or \(\frac{2 \pi}{T}=\sqrt{\frac{g}{a}}\) or \(T=2 \pi \sqrt{\frac{a}{g}}\)
TEST SERIES (PHYSICS FST)
266607
From a uniform disc of radius \(R\), a circular section of radius R \(/ 2\) is cut out. The centre of hole is a R/2 from the centre of the original disc. moment of inertia of resulting body about \(O_1\).
b \[ \begin{aligned} I_1 & =\frac{1}{2} M R^2+M\left(\frac{R}{2}\right)^2 \\ & =\frac{3}{4} M R^2 \end{aligned} \] \(\mathrm{I}_2=\frac{1}{2} \frac{M}{4}\left(\frac{\mathrm{R}}{2}\right)^2=\frac{1}{32} M \mathrm{R}^2\) Moment of inetia along point \(\mathrm{O}_1\) \(\mathrm{I}_1-\mathrm{I}_2\) \(=\frac{23}{32} \mathrm{MR}^2\)
