Question

The
second hand of a clock moves from position
12 to position 6 in 30 seconds. An ant starts from position 12 at same time that the hand is 12.
It travels to position 6 at same speed of the tip of the hand, but in straight line from 12 to 6.
The art arrives at position 6, "x" seconds before
the seconds hand. The closest number to "x" is
a)9 b) 10 c)11 d) 12​

Answer 1

Given :

Time taken by the second and of the clock to move from position 12 to 6 = 30 sec

The time taken by the ant to move from 12 to 6 in a straight line = (30 -x ) sec

The speed of the ant is same as the speed of the tip of the second hand .

To Find :

The closest number to x = ?

Solution :

Let the radius of the circular clock or length of the second hand be 'R'.

Since the tip of hand is moving in circular direction so the distance covered by it in moving from 12 to 6 = $\pi R$

And the ant  is moving in straight line, so distance covered by the ant is= 2R

Now the speed for tip of the hand and ant is same which is :

$v = \frac{\pi R }{30}$  ( since the time taken by tip to cover $\pi R$ is 30 sec )

So, the time taken by the ant  to cover $2 R$ distance with the speed $v = \frac{\pi R }{30}$

will be :

$=\frac{2R}{(\frac{\pi R}{30})}$

$=\frac{2R \times 30}{ \pi R}$

$=\frac{60}{\pi}$

= 19.10 sec

Now , since ant arrives x sec before , so :

x = 30 - 19.10

x = 10.90

So,  closest number to x is 10.

Answer 2

Answer:

Correct option is

D

2πmm/s,2

2

πmm/s

v=

T

2πr

v=

60

2π0.06

=2πmm/s

∣v

2

−v

1

∣=

(2π)

2

+(2π)

2

=2

2

π mm/s