Test Preparation on IIT-JEE solution Paper-2 (2013)

PART A - PHYSICS:

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring such that it is half-submerged in a liquid of density ∂  at the equilibrium position. The extension x₀ of the spring when it is in equilibrium is :

A metallic rod of length "l' is tied to a string of length 2l and made to rotate with angular speed w on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is:

This question has statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.

Statement - I: A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as f(1/2 mv²) then f=(m/M+m) 

Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Let [∈₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then :

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to α times its original magnitude, where α equals.

Two capacitors C₁ and C₂ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 103 kg/m3 and 2.2 × 1011 N/m2 respectively ?

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is :