Laws of Motion

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string

Two masses m₁ = 5 kg and m₂ = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure.

The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m₂ to stop the motion is

1. 23.3 kg
2. 43.3 kg
3. 10.3 kg
4. 18.3 kg

When forces F1, F2, F3 are acting on a particle of mass m

When forces F₁, F₂, F₃ are acting on a particle of mass m such that F₂ and F₃ are mutually perpendicular, then the particle remains stationary. If the force F₁ is now removed then the acceleration of the particle is

1. F₁/m
2. (F₂ - F₃)/m
3. (F₂F₃)/(mF₁)
4. F₂/m

Two forces are such that the sum of their magnitudes is 18 N

Two forces are such that the sum of their magnitudes is 18 N and their resultant is 12 N which is perpendicular to the smaller force. Then the magnitudes of the forces are

1. 10 N, 8 N
2. 12 N, 6 N
3. 13 N, 5 N
4. 16 N, 2 N

A spring balance is attached to the ceiling of a lift

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 m/s², the reading of the spring balance will be

1. 15 N
2. 24 N
3. 49 N
4. 74 N

A mass ‘m’ is supported by a massless string wound around a uniform

A mass ‘m’ is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?

1. g
2. 5g/6
3. g/2
4. 2g/3

A light string passing over a smooth light pulley connects two blocks

A light string passing over a smooth light pulley connects two blocks of masses m₁ and m₂ (vertically). If the acceleration of the system is g/8, then the ratio of the masses is

1. 5:3
2. 4:3
3. 8:1
4. 9:7

A block of mass m is placed on a surface with a vertical cross section given by y = x^3/6

A block of mass m is placed on a surface with a vertical cross section given by y = x³/6. If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is:

1. 1/6 m
2. 1/3 m
3. 1/2 m
4. 2/3 m

A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force

A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is:

1. ma
2. 2 ma
3. 3/2 ma
4. 5/3 ma

A point particle of mass m, moves along the uniformly rough track PQR

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals μ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR.

The values of the coefficient of friction μ and the distance x(=QR), are, respectively close to:

1. 0.2 and 3.5 m
2. 0.29 and 3.5 m
3. 0.29 and 6.5 m
4. 0.2 and 6.5 m