All Free Physics MCQs with Answers

61. A stone is whirled in a horizontal circle on a string. If the string suddenly breaks, the stone will

• A. fly radially outwards from the centre
• B. move along the tangent to the circle at the point of release
• C. fall straight down at once
• D. spiral outwards while slowing down

Explanation: With the centripetal force gone, no force acts horizontally and Newton's first law takes over, so the stone keeps the velocity it had at that instant, which is directed along the tangent. Gravity then curves the path downwards into a projectile trajectory. The belief that it flies straight outwards comes from thinking of centrifugal force as real.

62. At the top of a vertical circular loop, the minimum speed for a body to maintain contact with the track is given by

• A. v equals the square root of rg
• B. v equals rg
• C. v equals zero
• D. v equals the square root of 2rg

Explanation: At the critical speed the normal reaction falls to zero and gravity alone provides the centripetal force, so mg equals mv squared over r and v is the square root of rg. Any slower and the body leaves the track before reaching the top. This is the calculation behind loop the loop rides and the bucket of water swung overhead.

63. Angular displacement is measured in

• A. metres
• B. radians
• C. metres per second
• D. newtons

Explanation: The radian is the SI unit of angle, and because it is defined as a ratio of two lengths it is dimensionless, which is why the formula v equals r omega comes out in metres per second without any conversion factor. Degrees and revolutions are convenient in practice but must be converted to radians before use in these formulae. Linear displacement, by contrast, is measured in metres.

64. Two points lie on a rotating disc, one twice as far from the axis as the other. Compared with the inner point, the outer point has

• A. twice the angular speed and the same linear speed
• B. the same angular speed and twice the linear speed
• C. half the angular speed
• D. the same linear speed

Explanation: Every point on a rigid rotating body sweeps the same angle in the same time, so the angular speed is common to all of them. Linear speed is r omega, so doubling the radius doubles the speed along the arc. This is why the rim of a grinding wheel moves so much faster than a point near its centre.

65. Two forces of 3 N and 4 N act at right angles to each other. The magnitude of their resultant is

• A. 1 N
• B. 5 N
• C. 7 N
• D. 12 N

Explanation: For perpendicular vectors the resultant is the square root of (3 squared plus 4 squared), which is the square root of 25, giving 5 N. Adding the magnitudes to get 7 N would only be correct if the forces acted in the same direction, and 1 N is the result if they were exactly opposed. Every answer between 1 N and 7 N is possible depending on the angle.

66. Two forces of equal magnitude F act at an angle of 120 degrees to each other. Their resultant has magnitude

• A. 2F
• B. F times the square root of 3
• C. F
• D. zero

Explanation: Using the parallelogram rule, the resultant is the square root of (F squared plus F squared plus 2F squared cos 120), and since cos 120 is minus one half the last term cancels one of the others, leaving the square root of F squared, which is F. Equal vectors at 120 degrees are the arrangement in which three such vectors would sum to zero. At 0 degrees the resultant would be 2F and at 180 degrees it would be zero.

67. The minimum number of unequal coplanar forces whose vector sum can be zero is

• A. one
• B. two
• C. three
• D. four

Explanation: Two unequal forces can never cancel, since cancelling requires equal magnitudes in opposite directions. Three forces can close a triangle head to tail even when all three magnitudes differ, so three is the minimum. This is why the triangle of forces is the standard construction for a body in equilibrium under three forces.

68. A vector of magnitude 20 N acts at 30 degrees above the horizontal. Its horizontal component is

• A. 10 N
• B. 20 N
• C. 17.3 N
• D. 11.5 N

Explanation: The horizontal component is 20 cos 30, and cos 30 is 0.866, so the component is 17.3 N. The vertical component is 20 sin 30, which is 10 N, and that is the value offered as the distractor. Note that the components are always smaller than the vector itself, which is a quick sanity check.

69. If a vector has equal rectangular components, it makes an angle with the x axis of

• A. 30 degrees
• B. 45 degrees
• C. 60 degrees
• D. 90 degrees

Explanation: The angle is given by the inverse tangent of the ratio of the y component to the x component, and when the two are equal that ratio is 1, whose inverse tangent is 45 degrees. Each component then has magnitude equal to the vector divided by the square root of 2. At 90 degrees the x component would be zero rather than equal to the y component.

70. The scalar product of two vectors A and B is defined as

• A. AB sin theta, and the result is a vector
• B. AB cos theta, and the result is a scalar
• C. AB tan theta, and the result is a scalar
• D. AB, independent of the angle between them

Explanation: The dot product multiplies the magnitudes by the cosine of the angle between the vectors and gives a scalar, which is why work, the dot product of force and displacement, is a scalar. The sine form belongs to the vector product, whose result is a vector. The cosine factor is what makes the dot product zero for perpendicular vectors.