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JEE 2020 Physics: Mechanical Properties of Solids Quiz 1 (12.08.2019)
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Question 1
‘Young’s modulus’ is defined as the ratio of
Question 2
A lift of mass 'm' is connected to a rope which is moving upward with maximum acceleration `a'. For maximum safe stress, the elastic limit of the rope is 'T’. The minimum diameter of the rope is (g = gravitational acceleration)
Question 3
A metal rod of length and cross-sectional area 'A' is heated through 'T' °C. What is the force required to prevent the expansion of the rod lengthwise?
[Y = Young' s modulus of the material of rod.
- coefficient of linear expansion]
[Y = Young' s modulus of the material of rod.
- coefficient of linear expansion] Question 4
In an industry in order to increase the mechanical strength of steel a copper wire of length 1.1 m and steel wire of length 0.8 m, both of diameter 1.5 mm, are connected end to end. What will be the load applied when it is stretched by the load and the net elongation is found to be 0.7 mm? (Ys=2×1011 Nm-2& Yc=1.1×1011 Nm-2)
Question 5
A bottle has an opening of radius a and length b. A cork of length b and radius 
where 
is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is μ then the force needed to push the cork into the bottle is:
where is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is μ then the force needed to push the cork into the bottle is: Question 6
A steel rail of length 5 m and area of cross section 40 cm2 is prevented from expanding along its length while the temperature rises by 10°C. If coefficient of linear expansion and Young’s modulus of steel are 
and 
respectively, the force developed in the rail is approximately:
and respectively, the force developed in the rail is approximately:Question 7
A copper wire of length 2.2 m and a steel wire of length 1.6 m, both of diameter 3.0 mm are coneected end to end. When stretched by a force, The elongation in length 0.50 mm is produced in the copper wire. The stretching force is
(YCu = 1.1 ×1011 N/m2,
Ysteel= 2.0×1011 N/m2)
(YCu = 1.1 ×1011 N/m2,
Ysteel= 2.0×1011 N/m2)
Question 8
A trolley is initially moving towards right with velocity v0. Trolley stops after travelling distance ‘x’. Elastic string is attached to right end of trolley. Y= Young’s modulus of string. S = cross-section area of string. Find elongation in string (M = mass of string & L = natural length)
Question 9
Two wires A and B are of same materials. Their lengths are in the ratio 1 : 2 and diameters are in the ratio 2 : 1 when stretched by force FA and FB respectively they get equal increase in their lengths. Then the ratio FA/FB should be
Question 10
A rod is fixed between two points at 
. The coefficient of linear expansion of material of rod is 
and Young’s modulus is 
. Find the stress developed in the rod if temperature of rod becomes 
. The coefficient of linear expansion of material of rod is and Young’s modulus is . Find the stress developed in the rod if temperature of rod becomes
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