A uniform rod of length $L$ has a mass per unit length $\lambda$ and area of cross-section $A$. If the Young's modulus of the rod is $Y$. Then elongation in the rod due to its own weight is ...........
  • A$\frac{2 \lambda g L^2}{A Y}$
  • B$\frac{\lambda g L^2}{2 A Y}$
  • C$\frac{\lambda g L^2}{4 A Y}$
  • D$\frac{\lambda g L^2}{A Y}$
Medium
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    The length of wire becomes $l_1$ and $l_2$ when $100\,N$ and $120\,N$ tensions are applied respectively. If $10l_2=11l_1$, the natural length of wire will be $\frac{1}{x} l_1$. Here the value of $x$ is ........
    View Solution
  • 2
    When the temperature of a gas is $20^{\circ} C$ and pressure is changed from $P_1=1.01 \times 10^5 \,Pa$ to $P_2=1.165 \times$
    $10^5 \,Pa$, then the volume changes by $10 \%$. The Bulk modulus is $.........\times 10^5 \,Pa$
    View Solution
  • 3
    The isothermal elasticity of a gas is equal to
    View Solution
  • 4
    The upper end of a wire $1\,m$ long and $4\,mm$ radius is clamped. The lower end is twisted by an angle of $30^o$. The angle of shear is ...... $^o$
    View Solution
  • 5
    A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal is
    View Solution
  • 6
    Hooke's law is applicable for ....
    View Solution
  • 7
    Given below are two statements: one is labelled as Assertion$(A)$ and the other is labelled as Reason $(R).$

    $Assertion$ $(A)$ : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading.

    $Reason$ $(R)$ : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling.

    In the light of the above statements, choose the correct answer from the options given below :

    View Solution
  • 8
    An Indian rubber cord $L$ metre long and area of cross-section $A$ $metr{e^2}$ is suspended vertically. Density of rubber is $D$ $kg/metr{e^3}$ and Young's modulus of rubber is $E$ $newton/metr{e^2}$. If the wire extends by $l$ metre under its own weight, then extension $l$ is
    View Solution
  • 9
    A wire of cross-sectional area $3\,m{m^2}$ is first stretched between two fixed points at a temperature of $20°C$. Determine the tension when the temperature falls to $10°C$. Coefficient of linear expansion $\alpha = {10^{ - 5}}   { ^\circ}{C^{ - 1}}$ and $Y = 2 \times {10^{11}}\,N/{m^2}$  ........ $N$
    View Solution
  • 10
    A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to
    View Solution