A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and θ for the block to remain stationary on the wedge is

• $a = \frac{g}{\cos ec \theta }$

• $a= \frac{g}{\sin \theta }$

• a = g tan θ

• a = g cos θ

A cylindrical tube of uniform cross-sectional area A is fitted with two air tight frictionless pistons. The pistons are connected to each other by a metallic wire. Initially, the pressure of the gas is p0 and temperature is T0, atmospheric pressure is also p₀. Now, the temperature of the gas is increased to 2T₀, the tension of the wire will be

• 2p₀A

• p₀A

• p₀A/2

• 4p₀A

A skier starts from rest at point A and slides down the hill without turning or breaking. The friction coefficient is μ. When he stops at point B, his horizontal displacement is S. what is the height difference between points A and B?

(The velocity of the skier is small so that the additional pressure on the snow due to the curvature can be neglected. Neglect also the friction of air and the dependence of μ on the velocity of the skier.)

• h = μS

• h = μ/S

• h = 2μS

• h = μS²

A bicycle wheel rolls without slipping on the horizontal floor. Which one of the following is true about the motion of points on the rim of the wheel, relative to the axis at the wheel's centre?

• Points near the top move faster than points near the bottom

• Points near the bottom move faster than points near the top

• All points on the rim move with the same speed

• All points have the velocity vectors that are pointing in the radial direction towards the centre of the wheel