The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?
The planet Mars has two
moons, phobos and delmos. (i) phobos has
a period 7 hours, 39 minutes and an orbital
radius of 9.4 ×10³km. Calculate the mass
of mars. (ii) Assume that earth and mars
move in circular orbits around the sun,
with the martian orbit being 1.52 times
the orbital radius of the earth. What is
the length of the martian year in days ?
Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.
The length of the minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6 : 05 a m and 6 : 40 a m.
An archery target has three regions formed by three concentric circles as shown in Figure. If the diameters of the concentric circles are in the ratio 1: 2:3, then find the ratio of the areas of three regions.
Two uniform solid spheres
of equal radii R, but mass M and 4 M have
a centre to centre separation 6 R, as shown
in Fig. 7.10. The two spheres are held fixed.
A projectile of mass m is projected from the
surface of the sphere of mass M directly
towards the centre of the second sphere.
Obtain an expression for the minimum
speed v of the projectile so that it reaches
the surface of the second sphere.
All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm2. .(Use π = 3.14).
Find the potential energy of
a system of four particles placed at the
vertices of a square of side l. Also obtain
the potential at the centre of the square.
Three equal masses of m kg
each are fixed at the vertices of an
equilateral triangle ABC.
(a) What is the force acting on a mass 2m
placed at the centroid G of the triangle?
(b) What is the force if the mass at the
vertex A is doubled ?
Take AG = BG = CG = 1 m (see Fig. 7.5)
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