JEE Main Physics - Properties of Solids
Exam Duration: 60 Mins Total Questions : 30
A spring is stretched by applying a load to its free end. The strain produced in the spring is
- (a)
volumetric
- (b)
shear
- (c)
longitudinal and shear
- (d)
longitudinal
Upto which point on stress - strain graph of a metal wire, the material remains elastic?
- (a)
Proportional limit
- (b)
Yield point
- (c)
Ultimate point
- (d)
Breaking point
The maximum load which a wire can with stand without breaking, when its length is reduced to half of its original length, will
- (a)
be doubled
- (b)
be half
- (c)
be four times
- (d)
remains same
What would be the ratio of breaking maximum load of circular rod (radius r) to maximum load, if same rod is moulded into square rod of same length?
- (a)
\(1:1\)
- (b)
\(1:2\pi \)
- (c)
\(2:\pi \)
- (d)
\(\pi :2\)
A wire of length l is tied to the ceiling and weight w is tied to the lower end. If now put on pulley and weight w is attached to both sides of wire. Then, total extension in wire would be
- (a)
\(\Delta l\)
- (b)
\(2:\Delta l\)
- (c)
\(\frac { \Delta l }{ 2 } \)
- (d)
\(4:\Delta l\)
Two wires of the same length and same material but radii in the ratio of 1:2 are stretched by unequal forces to produce equal elongation. The ratio of two forces is
- (a)
\(1:4\)
- (b)
\(1:2\)
- (c)
\(2:1\)
- (d)
\(1:\sqrt { 2 } \)
How many elastic coefficients are required to describe the elastic properties of solids?
- (a)
1
- (b)
2
- (c)
3
- (d)
4
If a spherical ball is taken out from a deep pond, then its volume increases by 0.01%. If the bulk modulus of material is G=1010 N/m2. Then, the depth of pond should be (take, g=10 m/s2)
- (a)
1 m
- (b)
50 m
- (c)
1000 m
- (d)
100 m
A spring of constant K is cut into two parts of length in the ratio 2:3. The spring constant of larger spring is
- (a)
\(\frac { 5 }{ 3 } K\)
- (b)
\(\frac { 2 }{ 3 } K\)
- (c)
\(K\)
- (d)
\(\frac { 3 }{ 5 } K\)
A steel rod of Young's modulus 2X1011 N/m2 undergoes an elastic strain of 0.05%. The energy per unit volume stored in J/m3 is
- (a)
12500
- (b)
5000
- (c)
10000
- (d)
25000
If F is the force applied to an elastic bar to produce an extension of \(\Delta l.\) Then, the energy lost in the process is
- (a)
\(F.\Delta l\)
- (b)
\(\frac { F.\Delta l }{ 2 } \)
- (c)
\(zero\)
- (d)
\(\frac { 3F.\Delta l }{ 2 } \)
If the work done in stretching a wire by 1 mm is W. Then, the work required to stretch another wire of same material but with half the radius of cross - section and double the length by 2 mm is
- (a)
\(4W\)
- (b)
\(W\)
- (c)
\(\frac { 1 }{ 4 } W\)
- (d)
\(\frac { 1 }{ 2 } W\)
Which of the following correctly gives the elastic energy stored in the metal bar? ( \(\sigma \) =stress, \(\varepsilon \) =strain, Y=Young's modulus, L=length, \(\Delta l\) =extension, F=load, A=cross- sectional area).
- (a)
\(\frac { 1 }{ 2 } { \sigma }^{ 2 }Y\)
- (b)
\(\frac { 1 }{ 2 } \frac { { \sigma }^{ 2 } }{ Y } \)
- (c)
\(\frac { 1 }{ 2 } { \varepsilon }^{ 2 }Y.(AL)\)
- (d)
\(\frac { 1 }{ 2 } { \sigma }^{ 2 }Y.(AL)\)
A mass of 10 kg tied to the string which is fixed to the ceiling of the elevator. If the elevator is moving up with an acceleration of 5 m/s2 . Then the elastic energy stored in the wire is (given, area and length of wire are 5cm2 and 20 cm respectively and Young's modulus is 2X1011 N/m2 and use g=10 m/s2)
- (a)
4.5X10-5 J
- (b)
2.25X10-5 J
- (c)
1.125X10-5 J
- (d)
9X10-5 J
The maximum load a wire can with stand without breaking, when it is stretched to twice of its original length, will
- (a)
be half
- (b)
be four time decreased
- (c)
be double
- (d)
Information is insufficient
Consider the given mass-pulley system. If original length of string is l=3 m, Young's modulus of material is =2X1011 N/m2 and area of cross - section is 0.001 cm2 . Then, the final length (in m) of wire when it released from rest is
- (a)
3.0012
- (b)
3.0024
- (c)
3.0006
- (d)
3.001
If a change in temperature of 0.2 K changes the volume of one mole of ideal gas 1 atm pressure by 0.1 L. Then, the bulk modulus of gas is [use 1 atm = 105 N/m2]
- (a)
8.8X104 N/m2
- (b)
11.16X104 N/m2
- (c)
9.6X104 N/m2
- (d)
8.34X104 N/m2
One end of uniform rod of mass M, having cross- section area A is suspended from the roof and mass m is suspended from the other end. The stress at mid- point of rod is
- (a)
\(\frac { \left( m+\frac { M }{ 2 } \right) g }{ A } \)
- (b)
\(\frac { \left( \frac { m }{ 2 } +M \right) g }{ A } \)
- (c)
\(\frac { \left( m+M \right) g }{ A } \)
- (d)
\(\frac { \left( m+M \right) g }{ 2A } \)
Two rods X and Y of same material and same length having radii r1 and r2 respectively. If they are rigidly fixed at one end and twisted by same couple applied at free end, the ratio of angle of twist at end of X and the angle of twist at end of Y is
- (a)
\(\frac { { r }_{ 1 }^{ 2 } }{ { r }_{ 2 }^{ 2 } } \)
- (b)
\(\frac { { r }_{ 2 }^{ 2 } }{ { r }_{ 1 }^{ 2 } } \)
- (c)
\(\frac { { r }_{ 1 }^{ 4 } }{ { r }_{ 2 }^{ 4 } } \)
- (d)
\(\frac { { r }_{ 2 }^{ 4 } }{ { r }_{ 1 }^{ 4 } } \)
Match the physical quantities given in Column I with their formula in Column II and select correct option in the choices given below.
Column I | Column II | ||
A. | Elastic energy | 1. | \(-\frac { \Delta d }{ d } \times \frac { L }{ \Delta l } \) |
B. | Bulk modulus | 2. | \(\frac { 1 }{ 2 } \times Stress\times Strain\times Volume\) |
C. | Poisson's ratio | 3. | \(-\frac { \Delta p }{ \left( V\frac { \Delta V }{ } \right) } \) |
- (a)
A B C 3 2 1 - (b)
A B C 1 3 2 - (c)
A B C 1 2 3 - (d)
A B C 2 3 1
Two wires are made of the same material and have the same volume. However, wire 1 has cross- sectional area A and wire 2 has cross - sectional area 3A. If the length of wire 1 increases by \(\Delta x\) on applying force F, how much force is needed to stretch wire 2 by the same amount?
- (a)
F
- (b)
4F
- (c)
6F
- (d)
9F
If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is
- (a)
\(2{ S }^{ 2 }Y\)
- (b)
\(\frac { { S }^{ 2 } }{ 2Y } \)
- (c)
\(\frac { 2Y }{ { S }^{ 2 } } \)
- (d)
\(\frac { S }{ 2Y } \)
A wire fixed at the upper end stretches by length l by applying a force F. Then work done in stretching a wire is
- (a)
\(\frac { F }{ 2l } \)
- (b)
\(Fl\)
- (c)
\(2Fl\)
- (d)
\(\frac { Fl }{ 2 } \)