Mathematics Tes...

A pendulum bob is suspended on a flat car that moves with velocity v_o.The flat car is stopped by a bumper

(i) What is the angle through which the pendulum swings.

(ii) If the swing angle is\(\theta=60^{\circ}\) and \(l=10 \mathrm{m}\)what was the initial speed of the flat car?

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Two particles each of mass m are placed at A and C are such AB = BC = L. The gravitational force on the third particle placed at D at a distance L on the perpendicular bisector of the line AC is :

The gravitational potential of two homogeneous spherical shells of same surface density at their respective center are 3V and 4V. If the two shells coalesce into single one keeping surface density same, the potential at a point inside the shell is :

Two masses, 800kg and 450kg are at a distance 25m apart. The magnitude of gravitational field intensity at a point 20m distant from the 800kg mass and 15m distant from the 450kg mass is√x G (in N/kg). Then x is (where G is universal gravitational constant) :

The magnitude of gravitational field at distances r₁ and r₂ from the centre of a uniform sphere of radius R and mass M is given by  F1 and F2 respectively. Then which of the following is true?

(If r₁<R and r₂<R)

A particle hanging from a massless spring stretches it by 2 cm at earths surface. How much will the same particle stretch the spring at a height of 2624 km from the surface of the earth? (Radius of earth = 6400 km).

A particle hanging from a spring stretches it by 1cm at earth's surface. Radius of earth is 6400km. At a place 800km above the earths surface, the same particle will stretch the spring by-

A satellite is projected with a velocity √1.5 times its orbital velocity just above the earth's atmosphere. The initial velocity of the satellite is parallel to the surface. The maximum distance of the satellite from the earth will be:

The escape velocity for a planet is ve. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be :