Calculating Circle Circumference
The radius of the circle is given as $r = 21$ cm.
The formula for the circumference ($C$) of a circle is $C = 2 \pi r$. Using the approximation $\pi \approx \frac{22}{7}$, we calculate the circumference:
$C = 2 \times \frac{22}{7} \times 21 \text{ cm}$
$C = 2 \times 22 \times 3 \text{ cm}$
$C = 132 \text{ cm}$
Finding Triangle Side Length
The problem states that the circumference of the circle equals the perimeter of an equilateral triangle.
The perimeter ($P$) of an equilateral triangle with side length $s$ is $P = 3s$.
Equating the circumference and the perimeter:
$C = P$
$132 \text{ cm} = 3s$
To find the side length $s$, divide the perimeter by 3:
$s = \frac{132 \text{ cm}}{3}$
$s = 44 \text{ cm}$
The length of the side of the equilateral triangle is 44 cm.
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Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
