MCQOPTIONS
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MCQOPTIONS
This section includes 41 Mcqs, each offering curated multiple-choice questions to sharpen your BITSAT knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A slab is subjected to two forces F1 and F2 of same magnitude as shown in the figure. Force F2 is in xy-plane while force F1 acts along Z-axis at the point \(\left( {2\hat i + 3\hat j} \right).\) The moment of these forces about point O will be |
| A. | \(\left( {3\hat i + 2\hat j - 3\hat k} \right)F\) |
| B. | \(\left( {3\hat i - 2\hat j + 3\hat k} \right)F\) |
| C. | \(\left( {3\hat i - 2\hat j - 3\hat k} \right)F\) |
| D. | \(\left( {3\hat i + 2\hat j + 3\hat k} \right)F\) |
| Answer» C. \(\left( {3\hat i - 2\hat j - 3\hat k} \right)F\) | |
| 2. |
Particle undergoes uniform circular motion. About which point on the plane of the circle, the angular momentum of the particle will remains conserved? |
| A. | Centre of the circle |
| B. | On the circumference of the circle |
| C. | Inside the circle |
| D. | Outside the circle |
| Answer» B. On the circumference of the circle | |
| 3. |
A solid sphere & a hollow sphere of radius R are rolling down in inclined lane of height h. The ratio of velocities of solid sphere to Hollow sphere on reaching the bottom is |
| A. | \(\sqrt {\frac{{21}}{{25}}}\) |
| B. | \(\sqrt {\frac{{25}}{{21}}}\) |
| C. | \(\sqrt {\frac{3}{5}}\) |
| D. | \(\sqrt {\frac{5}{3}}\) |
| Answer» C. \(\sqrt {\frac{3}{5}}\) | |
| 4. |
If a disc has moment of inertia I about the axis which is tangential and in plane of the disc, then the moment of inertia about the axis which is tangential and perpendicular to its plane will be: |
| A. | \(\dfrac{6}{5}I\) |
| B. | \(\dfrac{3}{4}I\) |
| C. | \(\dfrac{3}{2}I\) |
| D. | \(\dfrac{5}{4}I\) |
| Answer» B. \(\dfrac{3}{4}I\) | |
| 5. |
If the radius of earth is 6400 km. then angular velocity for a point on its equator will be - |
| A. | 7.3 × 10-5 |
| B. | 7.3 × 10-6 |
| C. | 10 × 10-5 |
| D. | 1.5 × 10-5 |
| Answer» B. 7.3 × 10-6 | |
| 6. |
A uniform rectangular thin sheet ABCD of mass M has length ‘a’ and breadth ‘b’, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be: |
| A. | \(\left( {\frac{{3{\rm{a}}}}{4},\frac{{3{\rm{b}}}}{4}} \right)\) |
| B. | \(\left( {\frac{{5{\rm{a}}}}{3},\frac{{5{\rm{b}}}}{3}} \right)\) |
| C. | \(\left( {\frac{{2{\rm{a}}}}{3},\frac{{2{\rm{b}}}}{3}} \right)\) |
| D. | \(\left( {\frac{{5{\rm{a}}}}{{12}},\frac{{5{\rm{b}}}}{{12}}} \right)\) |
| Answer» E. | |
| 7. |
Moment of inertia of a thin circular ring of mass M and R rotating about an axis, passing through its centre and perpendicular to the plane is |
| A. | \(MR^2\) |
| B. | \(MR^2/4\) |
| C. | \(MR^2/2\) |
| D. | \((2/5) MR^2\) |
| Answer» B. \(MR^2/4\) | |
| 8. |
Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = \frac{{\rm{A}}}{{{{\rm{r}}^2}}}{{\rm{e}}^{ - 2{\rm{r}}/{\rm{a}}}}\), where A and a are constants. If Q is the total charge of this charge distribution, the radius R is: |
| A. | \({\rm{a}}\;{\rm{log}}\left( {1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}} \right)\) |
| B. | \(\frac{{\rm{a}}}{2}{\rm{log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\) |
| C. | \({\rm{a\;log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\) |
| D. | \(\frac{{\rm{a}}}{2}{\rm{log}}\left( {1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}} \right)\) |
| Answer» C. \({\rm{a\;log}}\left( {\frac{1}{{1 - \frac{{\rm{Q}}}{{2{\rm{\pi aA}}}}}}} \right)\) | |
| 9. |
A circular disc of radius b has a hole of radius ‘a’ at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{{\rm{r}}}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is: |
| A. | \(\sqrt {\frac{{{a^2} + {b^2} + ab}}{2}} \) |
| B. | \(\frac{{a + b}}{2}\) |
| C. | \(\sqrt {\frac{{{a^2} + {b^2} + ab}}{3}} \) |
| D. | \(\frac{{a + b}}{3}\) |
| Answer» D. \(\frac{{a + b}}{3}\) | |
| 10. |
In an experiment, electrons are accelerated, from rest by applying a voltage of 500 V. Calculate the radius of the path, if a magnetic field 100 mT is then applied.(Take, charge of the electron = 1.6 × 10-19 C and mass of the electron = 9.1 × 10-31 kg) |
| A. | 7.5 × 10-2 m |
| B. | 7.5 × 10-4 m |
| C. | 7.5 × 10-3 m |
| D. | 7.5 m |
| Answer» C. 7.5 × 10-3 m | |
| 11. |
A thin ring of mass 10 kg is rolling on the horizontal ground such that its center of mass has a velocity of 2 m/s. How much work (in joules) needs to be done to stop it? |
| A. | 40 |
| B. | 20 |
| C. | 10 |
| D. | 80 |
| Answer» B. 20 | |
| 12. |
An electric motor has a power rating of 3.3 kw. If its motor turns at a rate of 120 rev/min the torque of the shaft of the electric motor required for the purpose will be nearly |
| A. | 528 Nm |
| B. | 396 Nm |
| C. | 350 J |
| D. | 263 Nm |
| Answer» E. | |
| 13. |
In rotational motion, Power = Torque x ________. |
| A. | Angular velocity |
| B. | Angular momentum |
| C. | Angular displacement |
| D. | Angular acceleration |
| Answer» B. Angular momentum | |
| 14. |
A solid cylinder of mass 10 kg and radius 0.5 m is rotating about its axis at 20 rad/s. How much is it's kinetic energy (in joules)? |
| A. | 500 |
| B. | 250 |
| C. | 1000 |
| D. | 2000 |
| Answer» C. 1000 | |
| 15. |
For the apparent weight of body at equator to become zero, the earth rotate with an angular velocity of |
| A. | \(\sqrt {\frac{{2g}}{r}} \) |
| B. | \(\sqrt {\frac{g}{r}} \) |
| C. | \(\sqrt {\frac{g}{2r}} \) |
| D. | g/r |
| Answer» C. \(\sqrt {\frac{g}{2r}} \) | |
| 16. |
Maximum principal moment of inertia is |
| A. | the position of an area along which it can resist maximum force |
| B. | the position of an area along which it can resist maximum torque |
| C. | the position of an area along which it can resist maximum bending moment |
| D. | the position of an area along which it can resist maximum shear |
| Answer» D. the position of an area along which it can resist maximum shear | |
| 17. |
A proton and an α-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest rough a potential difference V. If a uniform magnetic field B is set up perpendicular to their velocities, the ratio of the radii rp : rα of the circular paths described by them will be |
| A. | \(1:\sqrt 2 \) |
| B. | \(1:\sqrt 3 \) |
| C. | 1 : 3 |
| D. | 1 : 2 |
| Answer» B. \(1:\sqrt 3 \) | |
| 18. |
A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be (Take, g = 10 m/s2) |
| A. | 8 kg – m2/s |
| B. | 3 kg – m2/s |
| C. | 2 kg – m2/s |
| D. | 6 kg – m2/s |
| Answer» E. | |
| 19. |
A thin disc of mass M and radius R has mass per unit area σ(r) = kr2 where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is: |
| A. | \(\frac{{M{R^2}}}{3}\) |
| B. | \(\frac{{2M{R^2}}}{3}\) |
| C. | \(\frac{{M{R^2}}}{6}\) |
| D. | \(\frac{{M{R^2}}}{2}\) |
| Answer» C. \(\frac{{M{R^2}}}{6}\) | |
| 20. |
A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5 s, is close to: |
| A. | 4.0 × 10-6 Nm |
| B. | 1.6 × 10-5 Nm |
| C. | 7.9 × 10-6 Nm |
| D. | 2.0 × 10-5 Nm |
| Answer» E. | |
| 21. |
If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is: |
| A. | \(\frac{{\;L}}{m}\) |
| B. | \(\frac{{4L}}{m}\) |
| C. | \(\frac{{\;L}}{{2m}}\) |
| D. | \(\frac{{\;2L}}{m}\) |
| Answer» D. \(\frac{{\;2L}}{m}\) | |
| 22. |
Angular momentum is ________. |
| A. | Moment of momentum |
| B. | Product of mass and angular velocity |
| C. | Product of moment of inertia and velocity |
| D. | Moment in angular motion |
| Answer» D. Moment in angular motion | |
| 23. |
A homogeneous solid cylindrical roller of radius R and mass m is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is |
| A. | \(\frac{F}{{2mR}}\) |
| B. | \(\frac{{2F}}{{3mR}}\) |
| C. | \(\frac{{3F}}{{2mR}}\) |
| D. | \(\frac{F}{{3mR}}\) |
| Answer» C. \(\frac{{3F}}{{2mR}}\) | |
| 24. |
A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of \(\frac{{7{\rm{M}}}}{8}\) and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I1 be the moment of inertia of the new sphere about its axis. The ratio \(\frac{{{{\rm{I}}_1}}}{{{{\rm{I}}_2}}}\) is given by: |
| A. | 185 |
| B. | 140 |
| C. | 285 |
| D. | 65 |
| Answer» C. 285 | |
| 25. |
A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ, where θ is the angle by which it has rotated, is given as kθ2. If its moment of inertia is I then the angular acceleration of the disc is: |
| A. | \(\frac{{\rm{k}}}{{4{\rm{I}}}}{\rm{\theta }}\) |
| B. | \(\frac{{\rm{k}}}{{{\rm{I}}}}{\rm{\theta }}\) |
| C. | \(\frac{{\rm{k}}}{{2{\rm{I}}}}{\rm{\theta }}\) |
| D. | \(\frac{{\rm{2k}}}{{{\rm{I}}}}{\rm{\theta }}\) |
| Answer» E. | |
| 26. |
A rigid square of loop of side 'a' and carrying current I2 is lying on a horizontal surface near a long current I1 carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be: |
| A. | Repulsive and equal to \(\frac{{{\mu _0}{I_1}{I_2}}}{{2\pi }}\) |
| B. | Attractive and equal to \(\frac{{{\mu _0}{I_1}{I_2}}}{{3\pi }}\) |
| C. | Repulsive and equal to \(\frac{{{\mu _0}{I_1}{I_2}}}{{4\pi }}\) |
| D. | Zero |
| Answer» D. Zero | |
| 27. |
An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then |
| A. | \(I' = \frac{3}{4}{I_0}\) |
| B. | \(I' = \frac{{15}}{{16}}{I_0}\) |
| C. | \(I' = \frac{{{I_0}}}{4}\) |
| D. | \(I' = \frac{9}{{16}}{I_0}\) |
| Answer» C. \(I' = \frac{{{I_0}}}{4}\) | |
| 28. |
A thin smooth rod of length L and mass M is rotating freely with angular speed ω0 about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod, will be: |
| A. | \(\frac{{M{\omega _0}}}{{M + m}}\) |
| B. | \(\frac{{M{\omega _0}}}{{M + 3m}}\) |
| C. | \(\frac{{M{\omega _0}}}{{M + 6m}}\) |
| D. | \(\frac{{M{\omega _0}}}{{M + 2m}}\) |
| Answer» D. \(\frac{{M{\omega _0}}}{{M + 2m}}\) | |
| 29. |
A rigid is made to rotate about an axis of rotation. Its moment of inertia about the axis of rotation depends on |
| A. | It angular momentum only |
| B. | Its angular velocity only |
| C. | The distribution of its mass about the axis about which it rotates, and also the orientation and position of this axis of rotation |
| D. | The torque applied only |
| Answer» D. The torque applied only | |
| 30. |
A rectangular coil (Dimension 5 cm × 2.5 cm) with 100 turns, carrying a current of 3 A in the clock-wise direction, is kept centered at the origin and in the X-Z plane. A magnetic field of 1 T is applied along X-axis. If the coil is tilted through 45° about Z-axis, then the torque on the coil is: |
| A. | 0.38 Nm |
| B. | 0.55 Nm |
| C. | 0.42 Nm |
| D. | 0.27 Nm |
| Answer» E. | |
| 31. |
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is θ, then: |
| A. | \({\rm{tan\;}}\theta = \frac{1}{{2\sqrt 3 }}\) |
| B. | \({\rm{tan\;}}\theta = \frac{2}{{\sqrt 3 }}\) |
| C. | \({\rm{tan\;}}\theta = \frac{1}{2}\) |
| D. | \({\rm{tan\;}}\theta = \frac{1}{3}\) |
| Answer» E. | |
| 32. |
A solid disc and a solid sphere have the same mass and same radius. Which one has the higher moment of inertia about its centre of mass? |
| A. | The disc |
| B. | The sphere |
| C. | Both have the same moment of inertia |
| D. | The information provided is not sufficient to answer the question |
| Answer» B. The sphere | |
| 33. |
An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is: |
| A. | \({\rm{\;}}\sqrt {\frac{{{\rm{qE}}}}{{{\rm{md}}}}} \) |
| B. | \({\rm{\;}}\sqrt {\frac{{2{\rm{qE}}}}{{{\rm{md}}}}} \) |
| C. | \({\rm{\;}}2\sqrt {\frac{{{\rm{qE}}}}{{{\rm{md}}}}} \) |
| D. | \({\rm{\;}}\sqrt {\frac{{{\rm{qE}}}}{{2{\rm{md}}}}} \) |
| Answer» C. \({\rm{\;}}2\sqrt {\frac{{{\rm{qE}}}}{{{\rm{md}}}}} \) | |
| 34. |
A thin circular plate of mass M and radius R has its density varying as ρ(r) = ρ0 r with ρ0 as constant and r is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is I = aMR2. The value of the coefficient ‘a’ is: |
| A. | 1/2 |
| B. | 3/5 |
| C. | 8/5 |
| D. | 3/2 |
| Answer» D. 3/2 | |
| 35. |
Biogas is a mixture of gases produced during decomposition of biomass necessarily in the: |
| A. | absence of oxygen |
| B. | presence of hydrogen |
| C. | absence of hydrogen |
| D. | presence of oxygen |
| Answer» B. presence of hydrogen | |
| 36. |
A thin ring of mass 5 kg and diameter 20 cm is rotating about its axis at 4200 rpm. Find its angular momentum (in kgm2/s)? |
| A. | 44 |
| B. | 11 |
| C. | 22 |
| D. | 33 |
| Answer» D. 33 | |
| 37. |
For a conservative holonomic dynamical system, the Lagrangian L, kinetic energy T and potential energy V are connected by |
| A. | L = T + V |
| B. | L = T - V |
| C. | L = 2T + V |
| D. | L = 2T - V |
| Answer» C. L = 2T + V | |
| 38. |
If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be: |
| A. | S1⁄2I3⁄2h-1 |
| B. | S1⁄2I1⁄2h-1 |
| C. | S1⁄2I1⁄2h0 |
| D. | S3⁄2I1⁄2h0 |
| Answer» D. S3⁄2I1⁄2h0 | |
| 39. |
A body is projected at t = 0 with a velocity 10 ms-1 at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms-2, the value of R is |
| A. | 10.3 m |
| B. | 2.8 m |
| C. | 5.1 m |
| D. | 2.5 m |
| Answer» C. 5.1 m | |
| 40. |
A horizontal platform is rotating with a uniform angular velocity around the vertical axis passing through its centre. At some instant a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall out. The angular velocity during the period |
| A. | decreases continuously |
| B. | decreases initially and increases again |
| C. | increases continuously |
| D. | increases initially and decreases again |
| Answer» C. increases continuously | |
| 41. |
A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO' passing through the centre of D1, as shown in the figure will be |
| A. | \(\frac{2}{3}M{R^2}\) |
| B. | \(\frac{4}{5}M{R^2}\) |
| C. | 3MR2 |
| D. | MR2 |
| Answer» D. MR2 | |