What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8 x 10^-4 J by the end of the second revolution after the beginning of the motion?

• 0.15 m/s²

• 0.18 m/s²

• 0.2 m/s²

• 0.2 m/s²

13.

Two non-mixing liquids of densities  and n (n >1) are put in a container. The height of each liquid is h. a solid cylinder of length L and density d is put in this container. The cylinder floats with its axis vertical and length pL (p<1) in the denser liquid. The density d is equal to,

• 
• 

• {1+(n-1)p}

• {1+(n-1)p}

Out of the following options which one can be used to produce a propagating electromagnetic wave?

• A stationary charge

• A chargeless particle

• An accelerating charge

• An accelerating charge

The charge following through a resistance R varies with time t as Q = at - bt², where a and b are positive constants. The total heat produced in R is,

• a³R/3b

• a³R/2b

• a³R/b

• a³R/b

Coefficient of linear expansion of brass and steel rods are  and . Lengths of brass and steel rods are l₁ and l₂ respectively. If (I₂ - I₁) is maintained same at all temperatures, which one of the following relations holds good?

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is,

• 100 cm

• 150 cm

• 200 cm

• 200 cm

The molecules of a given mass of a gas have r.m.s. velocity of 200 m/s at 27^o C and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are respectively, 127^_o C and 0.05 x 10⁵  Nm^-2, the RMS velocity of its molecules in m/s is,

A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced its half. Then,

• compressing the gas through adiabatic process will require more work to b done

• compressing the gas through isothermally or adiabatically will require the same amount of work.

• which of the case (whether compression through isohermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

• which of the case (whether compression through isohermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is [Latent heat of ice is 3.4 x 10⁵ J/kg and g =10 N/kg]

• 544 km

• 136 km

• 68 km

• 68 km