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A man grows into a giant such that his l...

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of

A

9

B

`(1)/(9)`

C

81

D

`(1)/(81)`

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Knowledge Check

  • A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming the his dimensity remains same, the stress in the leg will change by a factor of

    A
    9
    B
    `1/9`
    C
    81
    D
    `1/81`

  • A man has an antique pendulum clock of 1832 which bears the signature of the purchaser. He does not want to replace it in the fond memory of his great-grandparents. It ticks off one second in each side to side swing. It keeps correct time at 20^(@)C . The pendulum shaft is made of steel and its mass can be ignored as compared to the mass of the bob. Linear expansion coefficient of steel is 1.2xx10^(-5@)C^(-1) What is the fractional change in length if the shaft is cooled to 10^(@)C ?

    A
    0.0001
    B
    `1.2xx10^(-2)%`
    C
    `1.2xx10^(-3)%`
    D
    `1.2xx10^(-4)%`

  • Einstein established the idea of photons on the basis of Planck's quantum theory. According to his idea, the light of frequency f or wavelength lamda is infact a stream of photons. The rest mass of each photon is zero and velocity is equal to the velocity of light (c) = 3 xx 10^(8) m.s^(-1) . Energy, E = hf, where h = Planck's constant = 6.625 xx 10^(-34)J.s . Each photon has a momentum p = (hf)/(c) , although its rest mass is zero. The number of photons increase when the intensity of incident light increases and vice-versa. On the other hand, according to de Broglie any stream of moving particles may be represented by progressive waves. The wavelength of the wave (de Broglie wavelength) is lamda = (h)/(p) , where p is the momentum of the particle. When a particle having charge e is accelerated with a potential difference of V, the kinetic energy gained by the particle is K= eV. Thus as the applied potential difference is increased, the kinetic energy of the particle and hence the momentum increase resulting in a decrease in the de Broglie wavelength. Given, charge of electron, e = 1.6 xx 10^(-19)C and mass = 9.1 xx 10^(-31) kg . A proton is 1836 times heavier than an electron and has same charge as that of electron. For what velocity of the proton will its de Broglie wavelength be 4455 Å

    A
    `10^(6) m.s^(-1)`
    B
    `10^(7) m.s^(-1)`
    C
    `3 xx 10^(6) m.s^(-1)`
    D
    `3 xx 10^(7) m.s^(-1)`

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    If a man sells 7 horse and buys 9 cows his purchase increases by Rs. 176, but if he sells 13 cows and buys 9 horse decreases by Rs. 182 . Find the cost of a cow.

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