Physical Pendulum

Q.

The time period of two pendulums is in the ratio of 2:1. What will be the corresponding ratio of their lengths?

Q.

The time period of the two pendulums is 1.44 s and 0.36 s respectively. Calculate the ratio of their lengths.

Q.

The time periods of two simple pendulums are in the ratio of 4:1. What will be the corresponding ratio of their lengths?

Q.

A solid sphere (radius = R) rolls without slipping in a cylindrical through (radius = 5R). Find the time period of small oscillations.

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1. $2\pi \sqrt{\frac{28R}{5g}}$

2. $2\pi \sqrt{\frac{2R}{5g}}$

3. $2\pi \sqrt{\frac{8R}{5g}}$

4. $2\pi \sqrt{\frac{28R}{g}}$

Q. Can we use the mathematics of a simple pendulum to talk about a physical pendulum?

1. Yes
2. No

Q.

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.

1. $\frac{\sqrt{2}}{3}a$

2. $\frac{4\sqrt{2}}{3}a$

3. $\frac{9}{3}$

4. $\sqrt{2}$

Q.

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 $\frac{r}{2}$ away from the centre.

(i)$2\pi \sqrt{\frac{2\sqrt{2}a}{3g}}$ (ii) 1.51 sec (iii) $2\pi \sqrt{\frac{3r}{3g}}$ (iv)$T=2\pi \sqrt{\frac{2R}{g}}$

1. p - (i) ; q - (iii) ; r - (ii) ; s-(iv)

2. p - (ii) ; q - (iv) ; r - (i) ; s-(iii)

3. p - (ii) ; q - (i) ; r - (iii) ; s-(iv)

4. p - (iv) ; q - (iii) ; r - (ii) ; s-(i)

Q. A body is hindged about its centre of gravity. Will it move in any direction on being disturbed?

1. Yes
2. No

Q.

A disc is suspended at a point $\frac{R}{2}$ above its center, Find its period of oscillation.

1. $2\pi \sqrt{\frac{2g}{3R}}$

2. $2\pi \sqrt{\frac{2R}{3g}}$

3. $2\pi \sqrt{\frac{3R}{2g}}$

4. $2\pi \sqrt{\frac{R}{2g}}$

Q.

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 $\frac{r}{2}$ away from the centre.

(i)$2\pi \sqrt{\frac{2\sqrt{2}a}{3g}}$ (ii) 1.51 sec (iii) $2\pi \sqrt{\frac{3r}{3g}}$ (iv)$T=2\pi \sqrt{\frac{2R}{g}}$

1. p - (i) ; q - (iii) ; r - (ii) ; s-(iv)

2. p - (ii) ; q - (iv) ; r - (i) ; s-(iii)

3. p - (ii) ; q - (i) ; r - (iii) ; s-(iv)

4. p - (iv) ; q - (iii) ; r - (ii) ; s-(i)