If the radius of gyration of a compound pendulum about an axis through e.g. is more, then its frequency of oscillation will be

The periodic time of a compound pendulum is __________ when the distance between the point of suspension and the center of gravity is equal to the radius of gyration of the body about its center of gravity.

A

Zero

B

Minimum

C

Maximum

D

None of these

The periodic time of one oscillation for a simple pendulum is (where $$l$$ = Length of the pendulum.)

A

$$\frac{1}{{2\pi }}\sqrt {\frac{l}{{\text{g}}}} $$

B

$$\frac{1}{{2\pi }}\sqrt {\frac{{\text{g}}}{l}} $$

C

$$2\pi \sqrt {\frac{l}{{\text{g}}}} $$

D

None of these

The equivalent length of a simple pendulum which gives the same frequency as compound pendulum is

A

$$\frac{{\text{h}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$

B

$$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{\text{h}}}$$

C

$$\frac{{{{\text{h}}^2}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$

D

$$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{{{\text{h}}^2}}}$$

The length of a simple pendulum which gives the same frequency as the compound pendulum, is

A

$${\text{kG}} + {l_1}$$

B

$${\text{k}}{{\text{G}}^2} + {l_1}$$

C

$$\frac{{{\text{k}}{{\text{G}}^2} + l_1^2}}{{{l_1}}}$$

D

$$\frac{{{\text{kG}} + l_1^2}}{{{l_1}}}$$

The equivalent length of a simple pendulum which gives the same frequency as a compound pendulum is

A

$$\frac{{\text{h}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$

B

$$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{\text{h}}}$$

C

$$\frac{{{{\text{h}}^2}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$

D

$$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{{{\text{h}}^2}}}$$

The frequency of oscillation of a compound pendulum is

A

1/2π √g.h/k2G +h2

B

1/2π √k2G +h2/g.h

C

2π√g.h/k2G +h2

D

2π√k2G +h2/g.h

It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to

A

f

B

$$\frac{1}{{\text{f}}}$$

C

$$\frac{1}{{{{\text{f}}^2}}}$$

D

f²

The frequency of oscillation of a torsional pendulum is

A

2πkG/r √g/I

B

r/2πkG√g/I

C

2πkG/r√I/g

D

r/2πkG√I/g

To double the period of oscillation of a simple pendulum

A

The mass of its bob should be doubled

B

The mass of its bob should be quadrupled

C

Its length should be quadrupled

D

Its length should be doubled

The periodic time of one oscillation for a simple pendulum is

A

$$2\pi \sqrt {\frac{{\text{g}}}{l}} $$

B

$$\frac{1}{{2\pi }}\sqrt {\frac{{\text{g}}}{l}} $$

C

$$2\pi \sqrt {\frac{l}{{\text{g}}}} $$

D

$$\frac{1}{{2\pi }}\sqrt {\frac{l}{{\text{g}}}} $$

If the radius of gyration of a compound pendulum about an axis through e.g. is more, then its frequency of oscillation will be

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