Physical Pendulum
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A solid sphere (radius = R) rolls without slipping in a cylindrical through (radius = 5R). Find the time period of small oscillations.
2π√28R5g
2π√8R5g
2π√28Rg
2π√2R5g
A uniform square lamina of side 2a is hung up by one corner and oscillates in its own plane which is vertical. Find the length of the equivalent simple pendulum.
√23a
4√23a
93
√2
![](https://df0b18phdhzpx.cloudfront.net/ckeditor_assets/pictures/1039074/original_Dia_26.20.png)
- f=√2f0
- f=1√2f0
- f=√3f0
- f=f0
A uniform disc of radius r is to be suspended through a small hole made in the disc. Find the minimum possible time period of the disc for small oscillations. What should be the distance of the hole from the centre for it to have minimum time period?
2π√√2rgr2
√√2rgr√2
2π√√2rgr√2
2π√rgr2√2
A hollow sphere filled with water and one small hole at bottom is hung by a long thread and made to oscillates. What would be the effect on the period of oscillations as water slowly flows out of the hole at bottom?
First decreases then increases
Keep on increasing
First increases then decreases
Keeps on decreasing
A disc is suspended at a point R2 above its center, Find its period of oscillation.
2π√2g3R
2π√2R3g
2π√3R2g
2π√R2g
Find the time period of small oscillations of the following systems.
(p) A metre stick suspended through the 20 cm mark.
(q) A ring of mass m and radius r suspended through a point on its periphery.
(r) A uniform square plate of edge 'a' suspended through a corner.
(s) A uniform disc of mass m and radius r suspended through a point r2 away from the centre.
(i)2π√2√2a3g (ii) 1.51 sec (iii) 2π√3r3g (iv)T=2π√2Rg
p - (i) ; q - (iii) ; r - (ii) ; s-(iv)
p - (ii) ; q - (iv) ; r - (i) ; s-(iii)
p - (ii) ; q - (i) ; r - (iii) ; s-(iv)
p - (iv) ; q - (iii) ; r - (ii) ; s-(i)
A disc of radius R and mass M is pivoted at the rim and is set for small oscillations. If simple pendulum has to have the same period as that of the disc, the length of the simple pendulum should be