Q: Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2 R respectively, are joined end to end and a weight w is suspended from the combination as shown in the figure.

aligned & l_1= w L (4 R^2 ) Y , l_2= w L R^2 Y \\ & U= 1 2 K_1 ( l_1 )^2+ 1 2 K_2 ( l_2 )^2 \\ &= 1 2 Y (4 R^2 ) L [ w L 4 R^2 Y ]^2+ 1 2 Y ( R^2 ) L \\ & [ w L R^2 Y ]^2 ( K= Y A L ) \\ &= 5 w^2 L 8 R^2 Y aligned

Question 1

Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2 R respectively, are joined end to end and a weight w is suspended from the combination as shown in the figure.

Accepted Answer

aligned & l_1= w L (4 R^2 ) Y , l_2= w L R^2 Y \ & U= 1 2 K_1 ( l_1 )^2+ 1 2 K_2 ( l_2 )^2 \ &= 1 2 Y (4 R^2 ) L [ w L 4 R^2 Y ]^2+ 1 2 Y ( R^2 ) L \ & [ w L R^2 Y ]^2 ( K= Y A L ) \ &= 5 w^2 L 8 R^2 Y aligned

Question 2

With rise in temperature, the Young's modulus of elasticity:

Accepted Answer

Young's modulus, Y = Stress Strain If the temperature increases, strain also increases. Hence young's modulus decreases.

Question 3

Young's modules of materials of a wire of Length ' L ' and cross-sectional area A is Y . If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be:

Accepted Answer

Young's modulus depends on the material not depends on length and cross sectional area. So Young's modulus remains constant.

Question 4

Young's moduli of the material of wires A and B are in the ratio of 1: 4, while its area of cross sections are in the ratio of 1: 3. If the same amount of load is applied to both the wires, the amount

Accepted Answer

Elongation produced in the wire is given b L = FL AY Here, L= length of wire A= area of cross-section of wire Y = Young's moduli of material of wire. F and L is same and aligned & Y _ A Y _ B = 1 4 (given) \ & A _ A A _ B = 1 3 (given) \ & L _ A L _ B = A _ B A _ A Y _ B Y _ A = 3 1 4 1 =12 aligned

Question 5

A 100 ~m long wire having cross-sectional area 6.25 10^ -4 ~m ^2 and Young's modulus is 10^ 10 Nm ^ -2 is subjected to a load of 250 ~N , then the elongation in the wire will be :

Accepted Answer

= F Y A = 250 100 10^ 10 6.25 10^ -4 =40 10^ -4 ~m =4 10^ -3 ~m

Mechanical Properties of Solids — Previous Year Questions & Solutions