A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation is . If the coefficient of friction is , the highest distance above the x-axis at which the particle will be in equilibrium is

Two block of masses and are connected with a massless unstretched spring and placed over a plank moving with an acceleration ‘a’ as shown in figure. The coefficient of friction between the blocks and platform is .

In the arrangement shown in the figure mass of the block B and A are 2m,, 8m respectively. Surface between B and floor is smooth. The block B is connected to block C by means of a pulley. If the whole system is released then the minimum value of mass of the block C so that the block A remains stationary with respect to B is : (Co-efficient of friction between A and B is m.)

For lies in the interval

The following flow diagram represents the industrial preparation of nitric acid from ammonia

Answer the questions given below
Which line of entry describes the undefined reagents, products and reaction conditions?

Questions given below are based on the following experiment An oxyacid of phosphorus has the following properties Complete neutralization of the acid with sodium hydroxide solution gives an aqueous solution of sodium ion and oxy-acid anions in the ratio 2:1. When a solution of the acid is warmed with silver nitrate solution metallic silver is deposited What is the structure of the oxy-acid?

Read the following short write-up and answer the questions at the end of it The name ‘silica’ covers an entire group of minerals, which have the general formula the most common of which is quartz. Quartz is a framework silicate with tetrahedra arranged in spirals. The spirals can turn in a clockwise or anti-clockwise direction a feature that results in there being two mirror images, optically active, varieties of quartz The following pictures represent various silicate anions. Their formulae are respectively

Study the following sequence of reactions:

is

A particle is moved from (0, 0) to (a, a) under a force from two paths. Path 1 is OP and path 2 is OQP. Let and be the work done by this force in these two paths. Then:
S

In the figure shown all the surfaces are frictionless, and mass of the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10 by applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force in ground frame on the block in seconds is:

With what minimum velocity should block be projected from left end A towards end B such that it reaches the other end B of conveyer belt moving with constant velocity v? Friction coefficient between block and belt is .

A bob is suspended from a crane by a cable of length m. The crane and load are moving at a constant speed . The crane is stopped by a bumper and the bob on the cable swings out an angle of . The initial speed

If then

If then

If are in A.P. then and are in

In any 

s denotes the semi-perimeter of the triangle ABC, ∆ its area and R the radius of the circle circumscribing the triangle ABC i.e., R is the circum-radius.