Login/Sign Up
The wheel of a motor cycle is of radius \[35\] cm. How many revolutions per minute must the wheel make so as to keep a speed of \[66\] km/h?
The wheel of a motor cycle is of radius \[35\] cm. How many revolutions per minute must the wheel make so as to keep a speed of \[66\] km/h?
Areas Related to Circles | Exercise 11.3 | Maths | NCERT Exemplar
The wheel of a motor cycle is of radius \[35\] cm. How many revolutions per minute must the wheel make so as to keep a speed of \[66\] km/h?

From the question Radius of wheel = r = \[35\] cm

We know that one revolution of the wheel is equal to Circumference of the wheel

i.e., \[2\pi r\]

= \[2\times (22/7)\times 35\]

= \[220\] cm

But, from the question it is given that,

Speed of the wheel is \[66\] km/hr

= \[(66\times 1000\times 100)/60\] cm/min

= \[110000\] cm/min

∴ Number of revolutions in one min = \[110000/220=500\]

Therefore, \[500\] revolutions per minute should be  made by the wheel make so as to keep a speed of \[66\] km/h

i

More Material

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as 2 0 () – α = b wb w, where b is the verticle distance from the pole. w0 is a constant. Using Fermat’s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. Find the focal length.
(ii) A gravitational lens may be assumed to have a varying width of the form w(b) = k1 ln (k2/b) = k1 ln (k2/bmin). Show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius.
β = √(n-1)k1 u/v / u + v

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by n(r) = 1 + 2 GM/rc2 where r is the distance of the point of consideration from the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.