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To determine the composition of a bimeta...

To determine the composition of a bimetallic alloy, a sample is first weighed in air and then in water. These weights are found to be `w_1` and `w_2` respectively. If the densities of the two constituent metals are `rho_1 and rho_2` respectively, then the weight of the first metal in the sample is (where `rho_w` is the density of water)

A

`(rho_1)/(rho_w(rho_2 - rho_1))[w_1(rho_2 - rho_w) - w_2 rho_2]`

B

`(rho_1)/(rho_w(rho_2 + rho_1))[w_1(rho_2 - rho_w) + w_2 rho_2]`

C

`(rho_1)/(rho_w(rho_2 - rho_1))[w_1(rho_2 + rho_w) - w_2 rho_2]`

D

`(rho_1)/(rho_w(rho_2 - rho_1))[w_1(rho_1 - rho_w) - w_2 rho_1]`

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Knowledge Check

  • To determine the composition of a bimetallic alloy, a sample is first weighted in air and then in water. These weight are found to be omega_1 and omega_2 respectively. If the densities of the two constitunent metals are rho_1 and rho_2 respectively, then the weight of the first metal in the sample is (where rho _(omega) is the density of water)

    A
    `(rho_1)/(rho_(omega)(rho_2 - rho_1))[omega_1(rho_2 - rho_w)-rho_2 omega_2]`
    B
    `(rho_1)/(rho_(omega)(rho_2 +rho_1))[omega_1(rho_2 - rho_w)+rho_2 omega_2]`
    C
    `(rho_1)/(rho_(omega)(rho_2 - rho_1))[omega_1(rho_2 + rho_w)-rho_1 omega_2]`
    D
    `(rho_1)/(rho_(omega)(rho_2 - rho_1))[omega_1(rho_1 - rho_w)-rho_1 omega_2]`

  • To determine the composition of a bimetalic alloy, a sample is first weighed in air and then in water. These weights are found to be w_(1)andw_(2) respectively. If the densities of the two constituent metals are p_(1)andp_(2) respectively, then the weight of the first metal in the sample is (where rho_(w) is the density of water)

    A
    `rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)-rho_(w))-w_(2)rho_(2)]`
    B
    `rho_(1)/(rho_(w)(rho_(2)+rho_(1)))[w_(1)(rho_(2)-rho_(w))+w_(2)rho_(2)]`
    C
    `rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)+rho_(w))-w_(2)rho_(1)]`
    D
    `rho_(1)/(rho_(w)(rho_(2)-rho_(1)))[w_(1)(rho_(2)-rho_(w))-w_(2)rho_(1)]`

  • The planets with radii R_1 and R_2 have densities rho_1 and rho_2 respectively. Their atmospheric pressures are rho_1 and rho_2 respectively. Therefore the ratio of masses of their atmospheres neglecting variation of g within the limits of atmosphere is

    A
    `(rho_1R_2p_1)/(rho_2R_1p_2)`
    B
    `(p_1R_2rho_2)/(p_2R_1p_1)`
    C
    `(p_1R_1rho_1)/(p_2R_2rho_2)`
    D
    `(p_1R_1rho_2)/(p_2R_2rho_1)`

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