From the tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n times that taken by it to reach the highest point of its path. The relation between H,u and n is

• 2gH = n²u²

• gH = (n-2)²u²

• 2gH = nu²(n-2)²u²

• 2gH = nu²(n-2)²u²

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

• 2g/3

• g/2

• 5g/6

• 5g/6

3.

A block of mass m is placed on a surface with a vertical cross-section given by y = x³/6. If the coefficient of friction is 0.5, the maximum height above ground at which the block can be placed without slipping is 

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When a rubber band is strecthed by a distance x, it exerts a restoring force of magnitude F = ax +bx², where a and b are constants. The work done in stretching are unstretched rubber-band by L is

• aL² +bL²

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A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension

• angular momentum is conserved

• angular momentum changes in magnitude but not in the direction

• angular momentum changes in direction but not in magnitude

• angular momentum changes in direction but not in magnitude

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

• A meter scale.

• A vernier calliper where the 10 divisions in vernier scale match with 9 division in the main scale and main scale have 10 divisions in 1 cm.

• A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.

• A screw gauge having 100 divisions in the circular scale and pitch as 1 mm.

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100°C is (For steel Young’s modulus is 2×10¹¹ N m^–2 and coefficient of thermal expansion is 1.1×10^–5 K^–1 )

• 2.2 x 10⁸ Pa

• 2.2 x 10⁹ Pa

• 2.2 x 10⁷ Pa

• 2.2 x 10⁷ Pa

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 90^o angle at centre. Radius joining their interface makes an angle α with vertical. ratio d₁/d₂ is

On the heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom of the vessel. If r < < R and the surface tension of water is T, value of r just before bubbles detach is (density of water is ρ_w)