Floor of a room is of dimensions 5 m × 4 m and it is covered with circular tiles of diameters 50 cm each as shown in Figure. Find the area of floor that remains uncovered with tiles. (Use π = 3.14)
Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart ona horizontal table. What is the gravitational force and potential at the mid point ofthe line joining the centres of the spheres ? Is an object placed at that point inequilibrium? If so, is the equilibrium stable or unstable ?
On a square cardboard sheet of area 784 cm2, four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.
Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.
Two stars each of one solar mass (= 2×1030 kg) are approaching each other for a
head on collision. When they are a distance 109
km, their speeds are negligible.
What is the speed with which they collide ? The radius of each star is 104
km.
Assume the stars to remain undistorted until they collide. (Use the known value
of G).
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.
A satellite orbits the earth at a height of 400 km above the surface. How much
energy must be expended to rocket the satellite out of the earth’s gravitational
influence? Mass of the satellite = 200 kg; mass of the earth = 6.0×1024 kg; radius of
the earth = 6.4 × 106
m; G = 6.67 × 10–11 N m2 kg–2
.
In Figure. ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and distance between AB and DC = 14 cm. If arcs of equal radii 7 cm with centres A, B, C and D have been drawn, then find the area of the shaded region of the figure.
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