﻿ What is the minimum velocity with which a body of mass m must en

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# 11.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?

C.

The question is illustrated in the figure below,

Let, the tension at point A be TA.

Using Newton's second law, we have

Energy at point A =
Energy at point C is,

At point C, using Newton's second law,

In order to complete a loop, Tc
So,

From equation (i) and (ii)

Using the principle of conservation of energy,

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12.

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

4259 Views

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}

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14.

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

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15.

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

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16.

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?

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17.

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

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18.

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

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19.

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.

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20.

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

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