A thin $1 \,m$ long rod has a radius of $5\, mm$. A force of $50\,\pi kN$ is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is $0.01\, mm$, which of the following statements is false ?
  • AThe maximum value of $Y$ that can be determined is $10^{14}\,N/m^2$
  • B$\frac{{\Delta Y}}{Y}$ gets minimum contribution from the uncertainty in the length
  • C$\frac{{\Delta Y}}{Y}$ gets its maximum contribution from the uncertainty in strain 
  • D
    The figure of merit is the largest for the length of the rod.
JEE MAIN 2016, Diffcult
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
    Four identical rods are stretched by same force. Maximum extension is produced in
    View Solution
  • 2
    An $8\,m$ long copper wire and $4\,m$ long steel wire, each of cross section $0.5\,cm^2$ are fastened end to end and stretched by $500\,N$ force. The elastic potential energy of the system is (Youngs mod $: Y_{cu}= 1\times 10^{11}\,N/m^2,$ $Y_{steel} = 2\times 10^{11}\,N/m^2$ ) :
    View Solution
  • 3
    A sphere contracts in volume by $0.01 \%$ when taken to the bottom of sea $1 \,km$ deep. Find Bulk modulus of the material of sphere ........... $N / m ^2$
    View Solution
  • 4
    A composite heavy rope of two materials is suspended vertically from a high ceiling. The ratios of different quantities for upper to lower rope are length $\frac{{{L_u}}}{{{L_l}}} = \frac{1}{2}$ , cross sectional area $\frac{{{A_u}}}{{{A_l}}} = \frac{2}{1}$ ,density $\frac{{{d_u}}}{{{d_l}}} = \frac{2}{3}$ .What is the ratio of maximum stress in the two ropes
    View Solution
  • 5
    The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.
    View Solution
  • 6
    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
    View Solution
  • 7
    To break a wire of one meter length, minimum $40 \,kg \,wt$. is required. Then the wire of the same material of double radius and $6 \,m$ length will require breaking weight ....... $kg \,wt$
    View Solution
  • 8
    The area of cross section of the rope used to lift a load by a crane is $2.5 \times 10^{-4} m ^{2}$. The maximum lifting capacity of the crane is $10$ metric tons. To increase the lifting capacity of the crane to $25$ metric tons, the required area of cross section of the rope should be.$.........\times 10^{-4} \,m ^{2}$ (take $g =10\, ms ^{-2}$ )
    View Solution
  • 9
    The correct increasing order for modulus of elasticity for copper, steel, glass and rubber is
    View Solution
  • 10
    The pressure that has to be applied to the ends of a steel wire of length $10\ cm$ to keep its length constant when its temperature is raised by $100^o C$ is: (For steel Young's modulus is $2 \times 10^{11}$ $Nm^{-1}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}$ $K^{-1}$ )
    View Solution