Wires A and B are made from same material. A has twice diameter and three times length of B. If elas

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8.Mechanical Properties of Solids

medium

Wires $A$ and $B$ are made from the same material. $A$ has twice the diameter and three times the length of $B.$ If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in $A$ to that in $B$ is

$2:3$

$3:4$

$3:2$

$6:1$

Solution

(b) $U = \frac{1}{2}Fl = \frac{{{F^2}L}}{{2AY}}$. $U \propto \frac{L}{{{r^2}}}$ $(F$ and $Y$ are constant$)$

$\frac{{{U_A}}}{{{U_B}}} = \left( {\frac{{{L_A}}}{{{L_B}}}} \right) \times {\left( {\frac{{{r_A}}}{{{r_B}}}} \right)^2}$= $(3) \times {\left( {\frac{1}{2}} \right)^2} = \frac{3}{4}$

Standard 11

Physics

A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will be

medium

Identical springs of steel and copper are equally stretched. On which more work will have to be done ?

medium

A wire $2 \,m$ in length suspended vertically stretches by $10 \,mm$ when mass of $10 \,kg$ is attached to the lower end. The elastic potential energy gain by the wire is …… $J$ (take $g=10 \,m / s ^2$ )

easy

If a spring extends by $x$ on loading, then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant)

medium

(AIIMS-1997)

If the potential energy of a spring is $V$ on stretching it by $2\, cm$, then its potential energy when it is stretched by $10 \,cm$ will be

medium

Wires $A$ and $B$ are made from the same material. $A$ has twice the diameter and three times the length of $B.$ If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in $A$ to that in $B$ is

Solution

Similar Questions

A brass rod of cross-sectional area $1\,c{m^2}$ and length $0.2\, m$ is compressed lengthwise by a weight of $5\, kg$. If Young's modulus of elasticity of brass is $1 \times {10^{11}}\,N/{m^2}$ and $g = 10\,m/{\sec ^2}$, then increase in the energy of the rod will be

Identical springs of steel and copper are equally stretched. On which more work will have to be done ?

A wire $2 \,m$ in length suspended vertically stretches by $10 \,mm$ when mass of $10 \,kg$ is attached to the lower end. The elastic potential energy gain by the wire is …… $J$ (take $g=10 \,m / s ^2$ )

If a spring extends by $x$ on loading, then the energy stored by the spring is (if $T$ is tension in the spring and $k$ is spring constant)

If the potential energy of a spring is $V$ on stretching it by $2\, cm$, then its potential energy when it is stretched by $10 \,cm$ will be

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