MCQOPTIONS
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MCQOPTIONS
This section includes 12583 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2001. |
A plane flying horizontally at a height of 1500 m with a velocity of \[200\text{ m}{{\text{s}}^{-1}}\] passes directly overhead on antiaircraft gun. Then the angle with the horizontal at which the gun should be fired from the shell with a muzzle velocity of 400 \[\text{m}{{\text{s}}^{-1}}\]to hit the plane, is |
| A. | \[90{}^\circ \,\] |
| B. | \[60{}^\circ \] |
| C. | \[30{}^\circ \] |
| D. | \[45{}^\circ \] |
| Answer» C. \[30{}^\circ \] | |
| 2002. |
The equation of a projectile is \[y=\sqrt{3}x-\frac{\text{g}{{\text{x}}^{2}}}{20}\] The angle of projection is given by |
| A. | \[\text{tan}\theta \,\text{=}\frac{1}{\sqrt{3}}\] |
| B. | \[\text{tan}\theta \,\text{=}\,\sqrt{3}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | zero. |
| Answer» C. \[\frac{\pi }{2}\] | |
| 2003. |
The range of a projectile is R when the angle of projection is \[40{}^\circ \]. For the same velocity of projection and range, the other possible angle of projection is |
| A. | \[45{}^\circ \] |
| B. | \[50{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[40{}^\circ \] |
| Answer» C. \[60{}^\circ \] | |
| 2004. |
A particle of mass m is projected with a velocity u making an angle of \[30{}^\circ \] with the horizontal. The magnitude of\[({{V}_{h}}\times h)\] of the projectile when the particle is at its maximum height h |
| A. | \[\frac{\sqrt{3}}{2}\frac{{{\text{v}}^{\text{2}}}}{\text{g}}\] |
| B. | zero |
| C. | \[\frac{{{\text{v}}^{\text{2}}}}{\sqrt{2}\text{g}}\] |
| D. | \[\frac{\sqrt{3}}{16}\frac{{{\text{v}}^{\text{2}}}}{\text{g}}\] |
| Answer» E. | |
| 2005. |
A body is projected from the ground with a velocity at an angle of \[30{}^\circ \]. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground? [Take \[\text{g =10 m/}{{\text{s}}^{\text{2}}}\]] |
| A. | 50\[\sqrt{2}\] |
| B. | 70\[\sqrt{2}\] |
| C. | 15\[\sqrt{3}\] |
| D. | 16\[\sqrt{2}\] |
| Answer» B. 70\[\sqrt{2}\] | |
| 2006. |
Let two vectors \[\vec{A}=3\hat{i}+\hat{j}+2\hat{k}\] and\[\vec{B}=2\hat{i}-2\hat{j}+4\hat{k}\]. Consider the unit vector perpendicular to both A and B is |
| A. | \[\frac{\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\] |
| B. | \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\] |
| C. | \[\frac{-\hat{i}-\hat{j}-\hat{k}}{\sqrt{3}}\] |
| D. | \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\] |
| Answer» B. \[\frac{\hat{i}-\hat{j}-\hat{k}}{2\sqrt{3}}\] | |
| 2007. |
The vector having magnitude equal to 3 and perpendicular to the two vectors \[\vec{A}=2\hat{i}+2\hat{j}+\hat{k}\] and \[\vec{B}=2\hat{i}-2\hat{j}+3\hat{k}\] is: |
| A. | \[\pm \,(2\hat{i}-\hat{j}-2\hat{k})~~~\] |
| B. | \[\pm \,(3\hat{i}+\hat{j}-2\hat{k})\] |
| C. | \[-\,(3\hat{i}+\hat{j}-3\hat{k})~\] |
| D. | \[(3\hat{i}-\hat{j}-3\hat{k})\] |
| Answer» B. \[\pm \,(3\hat{i}+\hat{j}-2\hat{k})\] | |
| 2008. |
If the vectors \[(\hat{i}+\hat{j}+\hat{k})\] and \[3\hat{i}\] form two sides of a triangle, the area of the triangle is: |
| A. | \[\sqrt{3}\] |
| B. | \[2\sqrt{3}\] |
| C. | \[\frac{3}{\sqrt{2}}\] |
| D. | \[3\sqrt{2}\] |
| Answer» D. \[3\sqrt{2}\] | |
| 2009. |
If \[|\vec{a}|\,=4,\,\,|\vec{b}|\,=2\] and the angle between \[\vec{a}\] and \[\vec{b}\] is \[\pi /6\] then \[{{(\overrightarrow{a}\times \overrightarrow{b})}^{2}}\] is equal to |
| A. | 48 |
| B. | 16 |
| C. | 4 |
| D. | 2 |
| Answer» C. 4 | |
| 2010. |
If \[|\vec{A}\times \vec{B}|\,=\sqrt{3}\,\vec{A}\,.\,\vec{B}\,,\] then the value of \[|\vec{A}+\vec{B}|\] is: |
| A. | \[{{\left( {{\text{A}}^{\text{2}}}\text{+}{{\text{B}}^{\text{2}}}\text{+}\frac{\text{AB}}{\sqrt{\text{3}}} \right)}^{1/2}}\] |
| B. | \[\text{A+B}\] |
| C. | \[{{\left( {{\text{A}}^{\text{2}}}\text{+}{{\text{B}}^{\text{2}}}\text{+}\sqrt{\text{3}}\text{AB} \right)}^{1/2}}\] |
| D. | \[{{\left( {{\text{A}}^{\text{2}}}\text{+}{{\text{B}}^{\text{2}}}\text{+AB} \right)}^{1/2}}\] |
| Answer» E. | |
| 2011. |
If none of the vectors \[\vec{A},\,\,\vec{B}\] and \[\vec{C}\] are zero and if \[\vec{A}\times \vec{B}=0\],\[\vec{B}\times \vec{C}=0\] the value of \[\vec{A}\times \vec{C}\] is: |
| A. | unity |
| B. | zero |
| C. | \[{{B}^{2}}\] |
| D. | \[AC\text{ }cos\theta \] |
| Answer» C. \[{{B}^{2}}\] | |
| 2012. |
If \[{{V}_{1}}\] is velocity of a body projected from the point A and \[{{V}_{2}}\] is the velocity of a body projected from point B which is vertically below the highest point C. if both the bodies collide, then |
| A. | \[{{\text{V}}_{\text{1}}}\text{=}\frac{\text{1}}{\text{2}}{{\text{V}}_{\text{2}}}\] |
| B. | \[{{\text{V}}_{2}}\text{=}\frac{\text{1}}{\text{2}}{{\text{V}}_{1}}\] |
| C. | \[\,{{\text{V}}_{\text{1}}}\text{=}{{\text{V}}_{\text{2}}}\] |
| D. | Two bodies can't collide. |
| Answer» C. \[\,{{\text{V}}_{\text{1}}}\text{=}{{\text{V}}_{\text{2}}}\] | |
| 2013. |
The coordinates of a particle moving in x-y plane at any instant of time t are \[\text{x = 4}{{\text{t}}^{\text{2}}}\text{; y = 3}{{\text{t}}^{\text{2}}}\]. The speed of the particle at that instant is |
| A. | 10 t |
| B. | 5 t |
| C. | 3 t |
| D. | 2 t |
| Answer» B. 5 t | |
| 2014. |
A particle moves in the X-Y plane with a constant acceleration \[1.5\text{ }m/{{s}^{2}}\] in the direction making an angle of \[37{}^\circ \] with the X-axis. At \[t=0\] the particle is at the origin and its velocity is 8.0 m/s along the X-axis. Find the position of the particle at \[t=4.0\text{ }s\]. |
| A. | (41.6 m, 7.2 m) |
| B. | (50.3 m, 8.2 m) |
| C. | (60.2 m, 8.2 m) |
| D. | (11.2 m, 8 m) |
| Answer» B. (50.3 m, 8.2 m) | |
| 2015. |
The position of particle is given by \[\vec{r}=2\,{{t}^{2}}\widehat{i}+3\,t\widehat{j}+4\widehat{k},\] where \[t\] is in second and the coefficients have proper units for \[\vec{r}\] to be in meter. The \[\vec{a}\,(t)\] of the particle at \[t=1s\,\] is |
| A. | \[\text{4}\,\text{m }{{\text{s}}^{-2}}\] along y-direction |
| B. | \[\text{3}\,\text{m }{{\text{s}}^{-2}}\] along x-direction |
| C. | \[\text{4 m }{{\text{s}}^{-2}}\] along x-direction |
| D. | \[\text{2 m }{{\text{s}}^{-2}}\] along z-direction |
| Answer» D. \[\text{2 m }{{\text{s}}^{-2}}\] along z-direction | |
| 2016. |
A particle crossing the origin of co-ordinates at time t = 0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is \[\text{y = b}{{\text{x}}^{\text{2}}}\] (b is a constant), its velocity component in the x-direction is |
| A. | \[\sqrt{\frac{2\text{b}}{\text{a}}}\] |
| B. | \[\sqrt{\frac{\text{a}}{2\text{b}}}\] |
| C. | \[\sqrt{\frac{\text{a}}{\text{b}}}\] |
| D. | \[\sqrt{\frac{\text{b}}{\text{a}}}\] |
| Answer» C. \[\sqrt{\frac{\text{a}}{\text{b}}}\] | |
| 2017. |
The condition for \[\overrightarrow{A}+\overrightarrow{B}\] to be perpendicular to \[\overrightarrow{A}-\overrightarrow{B}\] is that |
| A. | \[|\overrightarrow{A}|\,\,=\,\,|\overrightarrow{B}|\] |
| B. | \[\overrightarrow{\text{A}}\,\,\text{=}\,\,\overrightarrow{\text{B}}\] |
| C. | \[\overrightarrow{\text{B}}\text{ =}\,\,\text{0 }\!\!~\!\!\text{ }\] |
| D. | \[\text{ }\!\!|\!\!\text{ }\,\overrightarrow{\text{A}}\,\text{+}\,\overrightarrow{\text{B}}\,\text{ }\!\!|\!\!\text{ }\,\,\text{= }\!\!|\!\!\text{ }\,\overrightarrow{\text{A}}-\overrightarrow{\text{B}}\,\,\text{ }\!\!|\!\!\text{ }\] |
| Answer» B. \[\overrightarrow{\text{A}}\,\,\text{=}\,\,\overrightarrow{\text{B}}\] | |
| 2018. |
If \[A=5\widehat{i}+7\widehat{j}-3\widehat{k}\] and \[B=2\widehat{i}+2\widehat{j}-a\widehat{k}\] are perpendicular vectors, the value of a is: |
| A. | \[-\,2\] |
| B. | 8 |
| C. | \[-\,7\] |
| D. | \[-\,8\] |
| Answer» E. | |
| 2019. |
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is |
| A. | 1 |
| B. | \[\sqrt{2}\] |
| C. | \[\sqrt{3}\] |
| D. | 2 |
| Answer» D. 2 | |
| 2020. |
If the magnitudes of vectors A, B and C are 12, 5 and 13 units respectively and A + B = C, the angle between vectors A and B is: |
| A. | 0 |
| B. | \[\pi \] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\frac{\pi }{4}\] |
| Answer» D. \[\frac{\pi }{4}\] | |
| 2021. |
The x and y components of \[\overrightarrow{\text{A}}\] are 4 m and 6 m, respectively. The x and y components of \[(\overrightarrow{A}+\overrightarrow{B}\,)\]are 10 m and 9 m respectively. The magnitude of vector B is: |
| A. | 19 m |
| B. | \[\sqrt{27}\] |
| C. | \[\sqrt{45}\] |
| D. | \[\sqrt{50}\] |
| Answer» D. \[\sqrt{50}\] | |
| 2022. |
The resultant of vectors \[\overrightarrow{\text{P}}\text{ }\]and \[\overrightarrow{\text{Q}}\] is \[\overrightarrow{\text{R}}\]. On reversing the direction of \[\overrightarrow{\text{Q}}\], the resultant vector becomes \[\overrightarrow{S}\]. Then, correct relation is |
| A. | \[~{{R}^{2}}+{{S}^{2}}=({{P}^{2}}+{{Q}^{2}})\] |
| B. | \[{{R}^{2}}+{{S}^{2}}={{P}^{2}}+{{Q}^{2}}\,\] |
| C. | \[{{R}^{2}}+{{P}^{2}}={{S}^{2}}+{{Q}^{2}}\] |
| D. | \[{{P}^{2}}+{{S}^{2}}=2\,({{Q}^{2}}+{{R}^{2}})\] |
| Answer» B. \[{{R}^{2}}+{{S}^{2}}={{P}^{2}}+{{Q}^{2}}\,\] | |
| 2023. |
If \[\overrightarrow{A}=\overrightarrow{B}-\overrightarrow{C}\], then, the angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is |
| A. | \[\text{ta}{{\text{n}}^{-1}}\frac{{{B}^{2}}+{{A}^{2}}-{{C}^{2}}}{2AB}\] |
| B. | \[{{\sin }^{-1}}\frac{{{B}^{2}}+{{A}^{2}}-{{C}^{2}}}{2AB}\] |
| C. | \[{{\cos }^{-1}}\frac{{{A}^{2}}+{{B}^{2}}-{{C}^{2}}}{2AB}\] |
| D. | \[{{\sec }^{-1}}\frac{{{A}^{2}}+{{B}^{2}}-{{C}^{2}}}{2AB}\] |
| Answer» D. \[{{\sec }^{-1}}\frac{{{A}^{2}}+{{B}^{2}}-{{C}^{2}}}{2AB}\] | |
| 2024. |
The resultant of two vectors \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is perpendicular to the vector \[\overrightarrow{A}\] and its magnitude is equal to half the magnitude of vector \[\overrightarrow{B}\]. The angle between \[\overrightarrow{A}\] and \[\overrightarrow{B}\] is |
| A. | \[120{}^\circ \] |
| B. | \[150{}^\circ \] |
| C. | \[135{}^\circ \] |
| D. | \[180{}^\circ \] |
| Answer» C. \[135{}^\circ \] | |
| 2025. |
The vector that must be added to the vector \[\widehat{i}-3\widehat{j}+2\widehat{k}\] and \[3\widehat{i}-6\widehat{j}+7\widehat{k}\] so that the resultant vector is a unit vector along the y-axis, is |
| A. | \[4\widehat{i}-2\widehat{j}+5\widehat{k~}~~\] |
| B. | \[-\,4\widehat{i}-2\widehat{j}+5\widehat{k~}~~\] |
| C. | \[3\widehat{i}-4\widehat{j}+5\widehat{k~}~~\] |
| D. | Null vector |
| Answer» C. \[3\widehat{i}-4\widehat{j}+5\widehat{k~}~~\] | |
| 2026. |
Vector \[\overrightarrow{A}\] makes equal angle with x, y and z-axis. Value of its components in terms of magnitude of \[\overrightarrow{A}\] will be |
| A. | \[\frac{\overrightarrow{A}}{\sqrt{3}}\] |
| B. | \[\frac{\overrightarrow{A}}{\sqrt{2}}\] |
| C. | \[\sqrt{3}\,\overrightarrow{A}\] |
| D. | \[\frac{\sqrt{3}}{\overrightarrow{A}}\] |
| Answer» B. \[\frac{\overrightarrow{A}}{\sqrt{2}}\] | |
| 2027. |
If the resultant of the vectors \[3\widehat{i}+4\widehat{j}+5\widehat{k}\] and \[5\widehat{i}\text{ }+\text{ }3\widehat{j}\text{ }+\text{ }4\widehat{k}\] makes an angle \[\theta \] with x-axis, then \[cos\text{ }90{}^\circ \] is |
| A. | 0.07 |
| B. | 0.574 |
| C. | 0.111 |
| D. | 0.123 |
| Answer» C. 0.111 | |
| 2028. |
Two identical particles are projected horizontally in opposite directions with a speed of \[5\text{ m}{{\text{s}}^{-1}}\] each from the top of a tall tower as shown. Assuming \[\text{g = 10 m}{{\text{s}}^{-2}}\], the distance between them at the moment when their velocity vectors become mutually perpendicular is |
| A. | 2.5 m |
| B. | 5 m |
| C. | 10 m |
| D. | 20 m |
| Answer» C. 10 m | |
| 2029. |
If a unit vector is represented by \[0.5\widehat{i}+0.8\widehat{j}+c\widehat{k}\,,\] then the value of c is |
| A. | 1 |
| B. | \[\sqrt{0.8}\] |
| C. | \[\sqrt{0.11}\] |
| D. | \[\sqrt{0.01}\] |
| Answer» D. \[\sqrt{0.01}\] | |
| 2030. |
The length of a metal is \[{{\ell }_{1}}\] when the tension in it is\[{{T}_{1}}\]and is\[{{\ell }_{2}}\]when the tension is\[{{T}_{2}}\]. The original length of the wire is |
| A. | \[\frac{{{\ell }_{1}}+{{\ell }_{2}}}{2}\] |
| B. | \[\frac{{{\ell }_{1}}{{T}_{2}}+{{\ell }_{2}}{{T}_{1}}}{{{T}_{1}}+{{T}_{2}}}\] |
| C. | (c)\[\frac{{{\ell }_{1}}{{T}_{2}}-{{\ell }_{2}}{{T}_{1}}}{{{T}_{2}}-{{T}_{1}}}\] |
| D. | \[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\] |
| Answer» D. \[\sqrt{{{T}_{1}}{{T}_{2}}{{\ell }_{1}}{{\ell }_{2}}}\] | |
| 2031. |
A circular tube of mean radius 8 cm and thickness 0.04 cm is melted up and recast into a solid rod of the same length. The ratio of the torsional rigidities of the circular tube and the solid rod is |
| A. | \[\frac{{{(8.02)}^{4}}-{{(7.98)}^{4}}}{{{(0.8)}^{4}}}\] |
| B. | \[\frac{{{(8.02)}^{2}}-{{(7.98)}^{2}}}{{{(0.8)}^{2}}}\] |
| C. | \[\frac{{{(0.8)}^{2}}}{{{(8.02)}^{4}}-{{(7.98)}^{4}}}\] |
| D. | \[\frac{{{(0.8)}^{2}}}{{{(8.02)}^{3}}-{{(7.98)}^{2}}}\] |
| Answer» B. \[\frac{{{(8.02)}^{2}}-{{(7.98)}^{2}}}{{{(0.8)}^{2}}}\] | |
| 2032. |
A spherical ball contracts in volume by 0.02% when subjected to a pressure of 100 atmosphere. Assuming one atmosphere \[={{10}^{5}}N{{m}^{-2}}\], the bulk modulus of the material of the ball is |
| A. | \[0.02\times {{10}^{5}}N/{{m}^{2}}\] |
| B. | \[0.02\times {{10}^{7}}N/{{m}^{2}}\] |
| C. | \[50\times {{10}^{7}}N/{{m}^{2}}\] |
| D. | \[50\times {{10}^{9}}N/{{m}^{2}}\] |
| Answer» E. | |
| 2033. |
Two, spring P and Q of force constants \[{{k}_{p}}\] and \[kQ\left( kQ=\frac{{{k}_{p}}}{2} \right)\] are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is |
| A. | E |
| B. | 2E |
| C. | E/2 |
| D. | E/4 |
| Answer» D. E/4 | |
| 2034. |
A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by t mm. The energy stored in the wire due to stretching is |
| A. | Zero |
| B. | 0.05 joule |
| C. | 100 joule |
| D. | 500 joule |
| Answer» C. 100 joule | |
| 2035. |
The Young's modulus of the material of a wire is \[2\times {{10}^{10}}N{{m}^{-2}}\]. If the elongation strain is 1 %, then the energy stored in the wire per unit volume in \[J{{m}^{-3}}\] is |
| A. | \[{{10}^{6}}\] |
| B. | \[{{10}^{8}}\] |
| C. | \[2\times {{10}^{6}}\] |
| D. | \[2\times {{10}^{8}}\] |
| Answer» B. \[{{10}^{8}}\] | |
| 2036. |
The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is |
| A. | \[\frac{B}{3p}\] |
| B. | \[\frac{3p}{B}\] |
| C. | \[\frac{p}{3p}\] |
| D. | \[\frac{p}{B}\] |
| Answer» D. \[\frac{p}{B}\] | |
| 2037. |
Two cylinders A and B of the same material have same length, their radii being in the ratio 1:2 respectively. The two are joined end to end as shown. One end of cylinder A is rigidly clamped while free end of cylinder B is twisted through an angle 9. The angle of twist of cylinder A is |
| A. | \[\frac{16}{17}\theta \] |
| B. | \[\frac{15}{16}\theta \] |
| C. | \[8\theta \] |
| D. | \[\frac{3}{2}\theta \] |
| Answer» B. \[\frac{15}{16}\theta \] | |
| 2038. |
Two Metal strips are riveted together at their ends by four rivets, each of diameter\[a=6\text{ }mm\]. The maximum tension that can be exerted by the riveted strip (if the Shearing stress on the rivet is not to exceed\[6.9\times \text{1}{{\text{0}}^{7}}Pa\]) is? |
| A. | \[6.8\times {{10}^{2}}N\] |
| B. | \[7.8\times {{10}^{3}}N\] |
| C. | \[8.28\times {{10}^{4}}N\] |
| D. | \[9.1\times {{10}^{3}}N\] |
| Answer» C. \[8.28\times {{10}^{4}}N\] | |
| 2039. |
Two parallel and opposite forces, each of magnitude 4000 N are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side. The angle of Shear is [shear modulas of metal is 80 G Pa] |
| A. | \[8\times {{10}^{-7}}rad\] |
| B. | \[7\times {{10}^{-7}}rad\] |
| C. | \[6\times {{10}^{-6}}rad\] |
| D. | \[5\times {{10}^{-5}}ra\] |
| Answer» B. \[7\times {{10}^{-7}}rad\] | |
| 2040. |
A body of mass 10 kg is attached to a wire of radius 3 cm. Its breaking stress is\[4.8\times {{10}^{7}}N{{m}^{-2}}\], the area of cross-section of the wire is\[{{10}^{-6}}{{m}^{2}}\] . What is the maximum angular velocity with which it can be rotated in the horizontal circle? |
| A. | \[1\,rad{{\sec }^{-1}}\] |
| B. | \[2\,rad{{\sec }^{-1}}\] |
| C. | \[4\,rad{{\sec }^{-1}}\] |
| D. | \[8\,rad{{\sec }^{-1}}\] |
| Answer» D. \[8\,rad{{\sec }^{-1}}\] | |
| 2041. |
A solid cube is subjected to a pressure of \[5\times {{10}^{5}}N{{m}^{-2}}\].Each side of the cube is shortened by 1 %. Find x if \[1.67\times {{10}^{x}}N/{{m}^{2}}\] be the bulk modulus of elasticity of the cube. |
| A. | 7 |
| B. | 11 |
| C. | 12 |
| D. | 15 |
| Answer» B. 11 | |
| 2042. |
A metal rod of Young's modulus \[2\times {{10}^{10}}N{{m}^{-2}}\] undergoes an elastic strain of 0.06%. The energy per unit volume stored in J m-3 is |
| A. | 3600 |
| B. | 7200 |
| C. | 10800 |
| D. | 14400 |
| Answer» B. 7200 | |
| 2043. |
When a force is applied on a wire of uniform cross-section area \[3\times {{10}^{-6}}{{m}^{2}}\] and length 4m, the increase in length is 1 mm. Energy stored in it will be (\[Y=2\times {{10}^{11}}N/{{m}^{2}}\]) |
| A. | 6250J |
| B. | 0.177J |
| C. | 0.075 J |
| D. | 0.150J |
| Answer» D. 0.150J | |
| 2044. |
The system is rotated with angular speed ox. (see figure). What is the ratio of energy stored in each wire? |
| A. | 1.29791666666667 |
| B. | 50:9 |
| C. | 1.96458333333333 |
| D. | 8:9 |
| Answer» C. 1.96458333333333 | |
| 2045. |
The Poisson's ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is: |
| A. | 1% |
| B. | 2% |
| C. | 0.025 |
| D. | 0.04 |
| Answer» C. 0.025 | |
| 2046. |
If in a wire of Young's modulus Y, longitudinal strain X is produced, then the value of potential energy stored in its unit volume will be |
| A. | \[Y{{X}^{2}}\] |
| B. | \[2Y{{X}^{2}}\] |
| C. | \[{{Y}^{2}}X/2\] |
| D. | \[Y{{X}^{2}}/2\] |
| Answer» E. | |
| 2047. |
Consider four steel wires of dimensions given below (d = diameter and / = length): \[l=1m,d=1mm\] \[l=2m,d=2mm\] \[l=2m,d=1mm\] \[l=1m,d=2mm\] If same force is applied to all the wires then the elastic potential energy stored will be maximum in wire: |
| A. | A |
| B. | B |
| C. | C |
| D. | D |
| Answer» D. D | |
| 2048. |
When a 4 kg mass is hung vertically on a light spring that obeys Hooke's law, the spring stretches by 2cms. The work required to be done by an external agent in stretching this spring by 5cms will be \[(g=9.8\text{ }m/se{{c}^{2}})\] |
| A. | 4.900joule |
| B. | 2.450joule |
| C. | 0.495 joule |
| D. | 0.245 joule |
| Answer» C. 0.495 joule | |
| 2049. |
A metal wire of length L is suspended vertically from a rigid support when the body of mass M is attached to the lower end of the wire, the elongation of the wire is\[l\]. The elastic potential energy stored in the wire is |
| A. | \[mgl\] |
| B. | \[mgl/2\] |
| C. | \[mgl/3\] |
| D. | \[mgl/4\] |
| Answer» C. \[mgl/3\] | |
| 2050. |
When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in \[dyne/c{{m}^{2}}\] is |
| A. | \[10\times {{10}^{12}}\] |
| B. | \[100\times {{10}^{12}}\] |
| C. | \[1\times {{10}^{12}}\] |
| D. | \[10\times {{10}^{12}}\] |
| Answer» D. \[10\times {{10}^{12}}\] | |