A metallic rod of length ‘l’ is tied to a string of length 2l and made to rotate with angular speed ω 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 
Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

• Statement – I is true, Statement – II is true, Statement – II is a correct explanation of Statement – I.

• Statement – I is true, Statement – II is true, Statement – II is not a correct explanation of Statement – I.

• Statement – I is true, Statement – II is false.

• Statement – I is true, Statement – II is false.

Let [ε₀] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then

• [ε₀] = [M^-1L^-3T²A]

• [ε₀] = [M^-1L^-3T⁴A²]

• [ε₀] =[M^-2L²T^-1A^-2]

• [ε₀] =[M^-2L²T^-1A^-2]

4.

A projectile is given an initial velocity of  where is along the ground and  is along the vertical. If g = 10 m/s², the equation of its trajectory is: 

• y = x-5x2

• y = 2x-5x²

• 4y = 2x- 5x²

• 4y = 2x- 5x²

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

• 5GmM/6R

• 2GmM/3R

• GmM/2R

• GmM/2R

A hoop of radius r and mass m rotating with an angular velocity ω₀
is placed on a rough horizontal surface.The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

• rω₀/4

• rω₀/3

• rω₀/2

• rω₀/2

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 σ at the equilibrium position. The extension x₀ of the spring when it is in equilibrium is

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

• 0.7

• 0.81

• 0.729

• 0.729

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 × 10¹¹N/m² respectively?

• 188.5 Hz

• 178.2 Hz

• 200.5 Hz

• 200.5 Hz

The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

• p_ov_o

• 
• 
•