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What featuring justifies the placing of prawns and grasshoppers in the same phylum

why graphite is poor than diamond?

why diamond is harder than graphite?

why graphite is smoother?

State whether the following statements are true or false. Justify your answer. a) The level curves of x/yz=are hyperbolas. b) 2222)0,0()y,x(yxyxlim+−→does not exist. c) The set }0z,0y,0x|)z,y,x{(<>>is a domain in 3R. d) The work done by the Force )x,y()y,x(F−=in moving a particle along the boundary of the ellipse 36y4x922=−+is 6. e) The function xyze)z,y,x(f=is integrable over ].1,0[]1,0[]1,0[××

A simple harmonic motion is represented by tatxw=cos)( Obtain expressions for velocity and acceleration of the oscillator. Also, plot the time variation of displacement, velocity and acceleration of the oscillator.

What should be the radius of a space station spinning with an angular speed of 2 rpm such that an astronaut inside the station experiences artificial gravity with g = 10 ms-2?

A pendulum bob of mass 50 g is suspended on a string from the ceiling of an elevator which is moving downwards with an acceleration 1.5 ms-2. Draw the free body diagram using the non-inertial frame of reference and determine the tension in the string. (Take g = 10 ms-2)

A satellite going around Earth in an elliptic orbit has a speed of 10 km s-1 at the perigee which is at a distance of 227 km from the surface of the earth. Calculate the apogee distance and its speed at that point.

A proton undergoes a head on elastic collision with a particle of unknown mass which is initially at rest and rebounds with 16/25 of its initial kinetic energy. Calculate the ratio of the unknown mass with respect to the mass of the proton.

A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in 10s. What would be the power required?

The position vector of two particles of mass 4.0 kg and 2.0 kg are, respectively, kjirˆ2ˆˆ321ttt++=r and ()kjirˆ4ˆ1ˆ322tt+-+=r where t is in seconds and the position in metres. Determine the position vector of the centre of mass of the system, the velocity of the cm and the net force acting on the system.

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