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.

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

A

Less

B

More

C

Same

D

Data are insufficient to determine same

When the body is suspended at the point of suspension, its periodic time and frequency will be ________ as compared to the body suspended at the point of percussion.

A

Same

B

Two times

C

Four times

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

Two circular dials of exactly the same size are mounted on a wall side by side in such a way that their perimeters touch at one point. Dial 1, which is on the left , spins clockwise around its center , and dial 2 , which is on the right spins counter clockwise around its center . (Assume that there is no friction at the point of contact between the dials.) Each dial is marked on its perimeter at three points that are at equale distances around the points arked ondial 1 are N, O, and P and the points marked on dial 2 are X, Y, and Z. If points O and Z are just meeting at the point of contact between the dials , and if dial 1 spins at the same speed as dial 2, what is the smallest number of revolutions of each dial that will bring O and Z together again?

A

1

B

2

C

3

D

4

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

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

Point A is 10 miles West of Point B. Point b is 30 miles North of pint C. Point C is 20 miles East of Point D. What is the distance (in miles) between Point A and Point D?

A

1010

B

1020

C

2010

D

3010

Point A is 10 km west of point B. Point B is 30 km north of point C. Point C is 20 km east of point D. What is the distance between point A and D?

A

1020Km

B

1010Km

C

2010Km

D

3010Km

The minimum periodic time of a compound pendulum is

A

$$\frac{1}{{2\pi }}\sqrt {\frac{{{{\text{k}}_{\text{G}}}}}{{\text{g}}}} $$

B

$$\frac{1}{{2\pi }}\sqrt {\frac{{{\text{2}}{{\text{k}}_{\text{G}}}}}{{\text{g}}}} $$

C

$$2\pi \sqrt {\frac{{{{\text{k}}_{\text{G}}}}}{{\text{g}}}} $$

D

$$2\pi \sqrt {\frac{{{\text{2}}{{\text{k}}_{\text{G}}}}}{{\text{g}}}} $$

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.

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