MCQOPTIONS
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MCQOPTIONS
This section includes 50 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mechanics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
A mass ‘M’ is suspended from a ceiling through a string of length ‘L’. This mass moves in a circle of horizontal radius ‘r’ at constant speed such that it is a conical pendulum. The tension in the string will be |
| A. | \(\frac{{mgL}}{{\left( {2\sqrt {{L^3} - {r^2}} } \right)}}\) |
| B. | \(\frac{{mgL}}{{\sqrt {{L^2}} }}\) |
| C. | \(mgL\sqrt {{r^2}} \) |
| D. | \(\frac{{mgL}}{{\sqrt {{L^2} - {r^2}} }}\) |
| Answer» E. | |
| 2. |
A ball is dropped from a height of 15 m above a metal platform. The ball strikes the platform and rebounds successively. The height of rebound after the first rebound is:(Coefficient of restitution can be taken as 0.8) |
| A. | 8.44 m |
| B. | 4.75 m |
| C. | 2.67 m |
| D. | 9.6 m |
| Answer» E. | |
| 3. |
If light and a heavy body have an equal kinetic energy of translation, then ________. |
| A. | Lighter body will have smaller momentum |
| B. | Heavy body will have smaller momentum |
| C. | Both will have same momentum |
| D. | Unpredictable |
| Answer» B. Heavy body will have smaller momentum | |
| 4. |
A projectile is projected from a point on ground with velocity of projection 'u' and angle of projection 'θ' . How much maximum height can the projectile reach ? |
| A. | \(h=\frac{u \sin \theta}{2g}\) |
| B. | \(h=\frac{u^2 \sin^2 \theta}{2g}\) |
| C. | \(h=\frac{u^2 \sin \theta}{2g}\) |
| D. | \(h=\frac{u \sin^2 \theta}{2g}\) |
| Answer» C. \(h=\frac{u^2 \sin \theta}{2g}\) | |
| 5. |
An artificial satellite revolves around the earth with a relative velocity of 800 m/s. If acceleration due to gravity is 9 m/s2 and gravitational force is 3600 N, then the mass of satellite is |
| A. | 4000 kg |
| B. | 400 N |
| C. | 400 kg |
| D. | 450 kg |
| Answer» D. 450 kg | |
| 6. |
A ball is falling freely from a height of 20 m then the velocity of ball when it reaches the ground at 20 m is (assume the acceleration of gravity as 10 m/s2 )? |
| A. | 40 m/s |
| B. | 30 m/s |
| C. | 10 m/s |
| D. | 20 m/s |
| Answer» E. | |
| 7. |
A car having weight W is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height h from the ground, midway between the front and rear wheels. The distance between the front and rear wheels is l. The acceleration of the car is a, and acceleration due to gravity is g. The reactions on the front wheels (Rf) and rear wheels (Rr) are given by |
| A. | \({{R}_{f}}={{R}_{r}}=\frac{W}{2}-\frac{W}{g}\left( \frac{h}{l} \right)a\) |
| B. | \({{R}_{F}}=\frac{W}{2}+\frac{W}{g}\left( \frac{h}{l} \right)a;{{R}_{r}}=\frac{W}{2}-\frac{W}{g}\left( \frac{h}{l} \right)a\) |
| C. | \({{R}_{F}}=\frac{W}{2}-\frac{W}{g}\left( \frac{h}{l} \right)a;{{R}_{r}}=\frac{W}{2}+\frac{W}{g}\left( \frac{h}{l} \right)a\) |
| D. | \({{R}_{f}}={{R}_{r}}=\frac{W}{2}+\frac{W}{g}\left( \frac{h}{l} \right)a\) |
| Answer» D. \({{R}_{f}}={{R}_{r}}=\frac{W}{2}+\frac{W}{g}\left( \frac{h}{l} \right)a\) | |
| 8. |
A man is standing in a lift and the lift is ascending with an upward acceleration 'f'. The man will appear to be heavier by |
| A. | (f + g) of his actual weight |
| B. | (f - g) of his actual weight |
| C. | fg of his actual weight |
| D. | \(\frac{f}{g}\) of his actual weight |
| Answer» E. | |
| 9. |
In elastic collisions of bodies: |
| A. | both of the momentum and total kinetic energy are conserved. |
| B. | neither momentum of the colliding bodies nor the total kinetic energy are recoverable. |
| C. | only the total kinetic energy is conserved. |
| D. | only the total momentum of the colliding objects is conserved |
| Answer» B. neither momentum of the colliding bodies nor the total kinetic energy are recoverable. | |
| 10. |
A ball of mass 1kg moving with the velocity of 2m/s collide directly with another stationary ball of mass 2kg and comes to rest after impact. The velocity of second ball after impact is: |
| A. | Zero |
| B. | 0.5 m/s |
| C. | 1.0 m/s |
| D. | 2.0 m/s |
| Answer» D. 2.0 m/s | |
| 11. |
A force vs extension graph of a spring is as shown. The work done in extending the spring is |
| A. | 10 J |
| B. | 5 J |
| C. | 5000 J |
| D. | 500 J |
| Answer» C. 5000 J | |
| 12. |
A particle starts from rest with a constant acceleration α m/sec2 and after some time it decelerates at a uniform rate of β m/sec2 till it comes to rest. If the total time taken between two rests positions is t, then maximum velocity acquired by the particle would be: |
| A. | \(\frac{{\alpha + \beta }}{2}t\) |
| B. | \(\frac{{\alpha - \beta }}{2}t\) |
| C. | \(\left( { \frac{{\alpha \beta }}{{\alpha + \beta }}} \right)t\) |
| D. | \(\left( {\frac{{\alpha + \beta }}{{\alpha - \beta }}} \right)t\) |
| Answer» D. \(\left( {\frac{{\alpha + \beta }}{{\alpha - \beta }}} \right)t\) | |
| 13. |
A particle of mass m is moving in a horizontal circle of radius r under the action of centripetal force expressed as \(-\frac{C}{r^2}\), where C is constant. The total energy of the particle is: |
| A. | \(\frac{C}{2r}\) |
| B. | \(-\frac{C}{2r}\) |
| C. | \(\frac{2C}{r}\) |
| D. | \(\frac{C}{r}\) |
| Answer» C. \(\frac{2C}{r}\) | |
| 14. |
In a rigid body in plane motion, the point R is accelerating with respect to point P at 10∠180° m/s2. If the instantaneous acceleration of point Q is zero, the acceleration (in m/s2) of point R is |
| A. | 8∠233° |
| B. | 10∠225° |
| C. | 10∠217° |
| D. | 8∠217° |
| Answer» E. | |
| 15. |
A point mass is shot vertically up from ground level with a velocity of 4 m/s at time, t = 0. It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is 10 m/s2 and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | ∞ |
| Answer» D. ∞ | |
| 16. |
A rotating fan completes 1200 revolutions every minute. If the tip of the blade is at a radius of 0.7 m, then the blade tip speed is (take π = 22/7) |
| A. | 44 m/s |
| B. | 22 m/s |
| C. | 66 m/s |
| D. | 88 m/s |
| Answer» E. | |
| 17. |
A point mass M is released from rest and slides down a spherical bowl (of radius R) from a height H as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is |
| A. | \(\sqrt {gH}\) |
| B. | \(\sqrt {2gR}\) |
| C. | \(\sqrt {2gH}\) |
| D. | 0 |
| Answer» D. 0 | |
| 18. |
A car moving with uniform acceleration covers 450 m in a 5 second interval and further it covers 700 m in a 10 second interval. The acceleration of the car is |
| A. | 7 m/s2 |
| B. | 50 m/s2 |
| C. | 25 m/s2 |
| D. | 10 m/s2 |
| Answer» E. | |
| 19. |
A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by r(t) = t2, θ(t) = t where t is time. The kinetic energy of the particle at time t = 2 is |
| A. | 4 |
| B. | 12 |
| C. | 16 |
| D. | 24 |
| Answer» D. 24 | |
| 20. |
A block is made to slide down an inclined plane (30° with horizontal) which is smooth. It starts sliding from rest and takes a time ‘t’ to reach the bottom of the plane. An identical body is freely dropped from the same point. The time the body takes to reach the bottom is |
| A. | t |
| B. | t/2 |
| C. | t/3 |
| D. | t/4 |
| Answer» C. t/3 | |
| 21. |
A point mass having mass M is moving with a velocity V at an angle θ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is |
| A. | -2MV cos θ ĵ |
| B. | 2MV sin θ ĵ |
| C. | 2MV cos θ ĵ |
| D. | -2MV sin θ ĵ |
| Answer» E. | |
| 22. |
A car crashes against a wall. The initial velocity at collision is 15 m/sec and the velocity after collision is 2.6 m/sec in the opposite direction. The mass of the car is 1500 kg. What is the average force exerted on the automobile bumper if collision lasts for 0.15 seconds. |
| A. | 1.76 × 105 N |
| B. | 2.1 × 105 N |
| C. | 2.76 × 105 N |
| D. | None of these |
| Answer» B. 2.1 × 105 N | |
| 23. |
A 1.0 kg ball drops vertically onto the floor with a speed of 25 m/s. It rebounds with an initial speed of 10 m/s. The impulse action on the ball during contact will be |
| A. | 15 N-s |
| B. | 25 N-s |
| C. | 35 N-s |
| D. | 45 N-s |
| Answer» D. 45 N-s | |
| 24. |
A particle is projected at an angle θ to the horizontal and it attains a maximum height H. The time taken by the projectile to reach the highest point, of its path is |
| A. | \(\frac{{\sqrt H }}{g}\) |
| B. | \(\sqrt {\frac{{2H}}{g}} \) |
| C. | \(\frac{{\sqrt {2H\sin \theta } }}{g}\) |
| D. | \(\frac{{\sqrt {2H} }}{{\sin \theta }}\) |
| Answer» C. \(\frac{{\sqrt {2H\sin \theta } }}{g}\) | |
| 25. |
A particle is projected with velocity u at an inclination θ with the horizontal. Then Maximum height (H) attained is |
| A. | \(\frac{u^2 sin^2\theta}{g}\) |
| B. | \(\frac{2u^2 sin^2\theta}{g}\) |
| C. | \(\frac{u^2 sin^2\theta}{2g}\) |
| D. | \(\frac{u^2 sin2\theta}{g}\) |
| Answer» D. \(\frac{u^2 sin2\theta}{g}\) | |
| 26. |
An elevator has an upward acceleration of 1 m/s2 What will be the force transmitted to the floor of the elevator by a man of weight 500 N travelling in the elevator? [g = 10 m/s2] |
| A. | 550 N |
| B. | 500 N |
| C. | 450 N |
| D. | 400 N |
| Answer» B. 500 N | |
| 27. |
A ball is projected up vertically with a velocity of 9.8 m/s. The time it takes to reach the ground is |
| A. | 0.5 s |
| B. | 4 s |
| C. | 2 s |
| D. | 9.8 s |
| Answer» D. 9.8 s | |
| 28. |
An astronaut finished some work “on the outside” of his satellite, which is in circular orbit around Earth. He leaves his wrench outside the satellite. The wrench will |
| A. | Fall directly down to Earth |
| B. | Continue in orbit at reduced speed |
| C. | Continue in orbit with the satellite |
| D. | Fly off tangentially into space |
| Answer» D. Fly off tangentially into space | |
| 29. |
On which of the fundamental principle a jet engine works? |
| A. | Conservation of mass only |
| B. | Conservation of energy only |
| C. | Conservation of linear momentum |
| D. | Conservation of mass and energy |
| Answer» D. Conservation of mass and energy | |
| 30. |
If a ball which is dropped from a height of 2.25 m on a smooth floor attains the height of bounce equal to 1.00 m, the coefficient of the restitution between the ball and the floor is equal to: |
| A. | 0.25 |
| B. | 0.5 |
| C. | 0.67 |
| D. | 0.33 |
| Answer» D. 0.33 | |
| 31. |
A person standing on a tower of height 60 m throws an object upwards with velocity of 40 m/s at an angle 30° to horizontal. Find the total time taken by the object to gain maximum height and fall on the ground (take g = 10 m/s2) |
| A. | 3 s |
| B. | 20 s |
| C. | 6 s |
| D. | 16 s |
| Answer» D. 16 s | |
| 32. |
An object is moving on a circular path of radius π meters at a constant speed of 4.0 m/s. The time required for one revolution is |
| A. | \(\frac{2}{{{\pi ^2}}}\;sec\) |
| B. | \(\frac{{{\pi ^2}}}{2}sec\) |
| C. | \(\frac{{{\pi}}}{2}sec\) |
| D. | \(\frac{{{\pi ^2}}}{4}sec\) |
| Answer» C. \(\frac{{{\pi}}}{2}sec\) | |
| 33. |
A pin jointed uniform rigid rod of weight W and Length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is |
| A. | zero |
| B. | W/4 |
| C. | W/2 |
| D. | W |
| Answer» C. W/2 | |
| 34. |
A car travelling at a constant speed of 36 km/hr in a circular path of radius 200 m, then normal acceleration and tangential acceleration in m/s2 is given by |
| A. | an = 0, at = 0 |
| B. | an = 0, at = 0.5 m/s2 |
| C. | an = 0.5 m/s2, at = 0 |
| D. | an = 0, at = 6.5 m/s2 |
| Answer» D. an = 0, at = 6.5 m/s2 | |
| 35. |
A body moves, from rest with a constant acceleration of 5 m per sec square. The distance covered in 5 sec is most nearly |
| A. | 38 m |
| B. | 62.5 m |
| C. | 96 m |
| D. | 124 m |
| Answer» C. 96 m | |
| 36. |
A shell is fired from a cannon with a speed ‘v’ at an angle θ with the horizontal direction as shown in the figure. At the highest point in its path, it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon. The speed of other piece immediately after the explosion is |
| A. | 3 v cos θ |
| B. | 2 v cos θ |
| C. | \(\frac{3}{2}\) v cosθ |
| D. | \(\sqrt{\frac{3}{2}}\)v cosθ |
| Answer» B. 2 v cos θ | |
| 37. |
A system of particles in motion has mass center G as shown in the figure. The particle i has mass mi and its position with respect to a fixed point O is given by the position vector ri. The position of the particle with respect to G is given by the vector ρi. The time rate of change of the angular momentum of the system of particles about G is(The quantity \({\ddot \rho _i}\) indicates the second derivative of ρi with respect to time and likewise for ri) |
| A. | \(\sum_i r_i\times m_i \ddot{\rho}_i\) |
| B. | \(\sum_i \rho_i \times m_i \ddot{r}_i\) |
| C. | \(\sum_i r_i \times m_i \ddot{r}_i\) |
| D. | \(\sum_i \rho_i \times m_i \ddot{\rho}_i\) |
| Answer» C. \(\sum_i r_i \times m_i \ddot{r}_i\) | |
| 38. |
If g1 and g2 are the gravitational acceleration on two mountains A and B respectively, then the weight of body when transported from A to B will be multiplied by |
| A. | Factor g1 |
| B. | Factor g2 |
| C. | Factor (g1/g2) |
| D. | Factor (g2/g1) |
| Answer» E. | |
| 39. |
A ball is dropped from a height of 10 m on a smooth floor and after the impact, the ball bounces to a height of 2.5 m. The coefficient of restitution between the ball and the floor is |
| A. | 0.25 |
| B. | 0.33 |
| C. | 0.67 |
| D. | 0.5 |
| Answer» E. | |
| 40. |
If the horizontal range of a projectile is maximum then the angle of the projectile must be ______ with horizontal. |
| A. | 90° |
| B. | 75° |
| C. | 45° |
| D. | 30° |
| Answer» D. 30° | |
| 41. |
'If 'θ' is angle of projection and 'u' is velocity of projection for a projectile, then its horizontal range is given by- |
| A. | R = (u2sin2θ) / g |
| B. | R = (u2cosθ) / g |
| C. | R = (u2cos2θ) / g |
| D. | R = (u2sinθ) / g |
| Answer» B. R = (u2cosθ) / g | |
| 42. |
A body moves, from rest with a constant acceleration of 5 m per sec2. The distance covered in 10 sec is most nearly |
| A. | 200 m |
| B. | 300 m |
| C. | 250 m |
| D. | 500 m |
| Answer» D. 500 m | |
| 43. |
If the momentum of a body increases from 10 units to 25 units in 5 sec, then the force acting on it is |
| A. | 1 unit |
| B. | 2 units |
| C. | 3 units |
| D. | 4 units |
| Answer» D. 4 units | |
| 44. |
A body starting from rest moves in a straight line with its equation of motion being.s = 2t3 – 3t2 + 2t + 1Where s is displacement in m and t is time in s. Its acceleration after one second is |
| A. | 6 m/s2 |
| B. | 2 m/s2 |
| C. | 12 m/s2 |
| D. | 3 m/s2 |
| Answer» B. 2 m/s2 | |
| 45. |
A railway wagon A of mass 10000 kg collides with another identical wagon B as shown in the figure. If A is moving at 5 m/s and B is at rest at the time of collision, the maximum compression in the spring S with a spring constant of 2 MN/m will be |
| A. | 20 cm |
| B. | 30 cm |
| C. | 35 cm |
| D. | 45 cm |
| Answer» D. 45 cm | |
| 46. |
A projectile is fired at an angle θ to the vertical. Its horizontal range will be maximum when θ is |
| A. | 30° |
| B. | 45° |
| C. | 60° |
| D. | 90° |
| Answer» C. 60° | |
| 47. |
A motorist is driving at 25 m/s on the curved road of radius 500 m. He suddenly applies the brakes and that causes the speed to decrease to 15 m/s at the constant rate in 10 seconds. What will be the tangential component (at) and the normal component (an) of acceleration immediately after the application of brakes |
| A. | at = -1 m/s2, an =1 m/s2 |
| B. | at = -1m/s2, an = 1.25 m/s2 |
| C. | at = -1.25 m/s2, an = 1 m/s2 |
| D. | at = -1.25 m/s2, an = 2 m/s2 |
| Answer» C. at = -1.25 m/s2, an = 1 m/s2 | |
| 48. |
Impulse can be obtained from the- |
| A. | Velocity-time diagram |
| B. | Force-displacement diagram |
| C. | Velocity-displacement diagram |
| D. | Force-time diagram |
| Answer» E. | |
| 49. |
An elevator has a mass of 5000 kg. When the tension in the supporting cable is 60 kN, the acceleration of the elevator is nearly |
| A. | 8 m/s2 |
| B. | 12 m/s2 |
| C. | -2 m/s2 |
| D. | 2 m/s2 |
| Answer» E. | |
| 50. |
An object having 10 kg mass weighs 5 N on a planet. The value of ‘g’ at this planet is |
| A. | 0.5 m/sec2 |
| B. | 4.9 m/sec2 |
| C. | 10.2 m/sec2 |
| D. | 9.7 m/sec2 |
| Answer» B. 4.9 m/sec2 | |