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Time Period

Time Period

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Q. Two simple pendulums whose lengths are \(100~\text{cm}\) and \(121~\text{cm}\) are suspended side by side. Their bobs are pulled together and then released. After how many minimum oscillations of the longer pendulum, will the two be in phase again.

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Q.

Two racing cars of masses $m_{1} a n d m_{2}$ are moving in circles of radii $r_{1} a n d r_{2}$ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

$m_{1} : m_{2}$
$r_{1} : r_{2}$
$1 : 1$
$m_{1} r_{1} : m_{2} r_{2}$

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Q. An athlete completes one round of a circular track of radius 10 m in 40 sec. The distance covered by him in 2 min 20 sec is

70 m
140 m
110 m
220 m

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Q.

Two racing cars of masses $m_{1} a n d m_{2}$ are moving in circles of radii $r_{1} a n d r_{2}$ respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

$m_{1} : m_{2}$
$r_{1} : r_{2}$
$1 : 1$
$m_{1} r_{1} : m_{2} r_{2}$

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Q.

The angular speed of seconds needle in a mechanical watch is

$\frac{π}{30} r a d / s$
$2 π r a d / s$
$π r a d / s$
$\frac{60}{π} r a d / s$

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Q. Find the time period of meeting of the minute hand and second hand of a clock. (Initial positions are shown in the figure below)

$\frac{59}{60} min$
$\frac{60}{59} min$
$\frac{3}{4} min$
$\frac{3}{8} min$

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Q. A clock is in x- y plane. Find angular velocity of second hand of a clock (in rad/s).

$\frac{π}{30} (^i)$
$\frac{π}{30} (-^j)$
$\frac{π}{60} (^k)$
$\frac{π}{30} (-^k)$

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Q. Two particles

A

and

B

are moving in a uniform circular motion in concentric circles of radius

r_{A}

and

r_{B}

with speed

v_{A}

and

v_{B}

respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be

$r_{A} : r_{B}$
$v_{A} : v_{B}$
$r_{B} : r_{A}$
$1 : 1$

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Q. A toy car travels in a horizontal circle of radius

2 a

. It is kept on the track by a radial elastic string of unstretched length

a

. The period of rotation of the toy car is

T_{0}

. Now, the toy car is speeded up until it is moving in a circle of radius

3 a

. Assuming that the string obeys Hooke's law, find the new period

T

in terms of

T_{0}

.

$T = T_{0}$
$T = \frac{\sqrt{3}}{2} T_{0}$
$T = \frac{2 T_{0}}{\sqrt{3}}$
$T = \frac{3}{4} T_{0}$

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Q.

The angular speed of seconds needle in a mechanical watch is

$\frac{π}{30} r a d / s$
$2 π r a d / s$
$π r a d / s$
$\frac{60}{π} r a d / s$

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