Laws of Motion

A body under the action of a force F = 6î –8ĵ+10k, acquires an acceleration of 1 m/s². The mass of this body must be

The mass of a lift is 2000 kg. When the tension in the supporting cable is 28000 N, then its acceleration is

A particle moves in a circle of radius 5cm with constant speed and time period 0.2πs. The acceleration of the particle is

With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is 2/3 of the weight?

A body of mass 0.25 kg is projected with muzzle velocity 100 m/s from a tank of mass 100 kg. What is the velocity of the tank?

A machine gun fires 10 bullets/s, each of mass 10g, the speed of each bullet is 20 cms⁻¹, then force of recoil is

A boat of mass 40 kg is at rest. A dog of mass 4 kg moves in the boat with a velocity of 10 ms⁻¹. What is the velocity of boat?

What determines the nature of the path followed by the particle?

A stone is tied to a string of length l and whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is

A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/s. The tension in the string is 6 N, when the stone at (take,g=10 m/s²).

A particle is kept at rest at the top of a sphere of diameter 42 m. When disturbed slightly, it slides down. At what height h from the bottom, the particle will leave the sphere?

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 ms⁻², the reading of the spring balance will be

A car is moving in a circular horizontal track of radius 10.0 m with a constant speed of 10.0 ms⁻¹. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with the track is (take,g = 10 ms⁻²)

A conveyor belt is moving at a constant speed of 2 m/s. A box is gently dropped on it. The coefficient of friction between them is µ = 0.5. The distance that the box will move relative to belt before coming to rest on it taking g = 10 ms⁻², is

A national roadway bridge over a canal is in the form of an arc of a circle of radius 49 m. What is the maximum speed with which a car can move without leaving the ground at the highest point? (take, g= 9.8 ms⁻²)

A ship of mass 3 x 10⁷ kg initially at rest is pulled by a force of 5 x 10⁴ N through a distance of 3 m. Assume that the resistance due to water is negligible, the speed of the ship is

The ratio of the weight of a man in a stationary lift and when it is moving downwards with uniform acceleration a is 3:2, then the value of a is

A stone of mass 1 kg tied to a light inextensible string of length L=10/3 is whirling in a circular path of radius L in vertical plane. If the ratio of the maximum tension to the minimum tension in the string is 2, what is the speed of stone at the highest point of the circle? (Take ,g=10 ms⁻²)

A spring balance is attached to the ceiling of lift. A man hangs his bag on the string and the balance reads 49 N, when the lift is stationary. If the lift moves downwards with an acceleration of 5 ms⁻². The reading of the spring balance would be

A block of mass 4 kg is kept on a rough horizontal surface. The coefficient of static friction is 0.8. If a force of 19 N is applied on the block parallel to the floor, then the force of friction between the block and floor is

Sand is being dropped on a conveyor belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be:

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is

A heavy uniform chain lies on a horizontal top of table. If the coefficient of friction between the chain and the table is 0.25, then the maximum percentage of the length of the chain that can hang over one edge of the table is

A block is moving up an inclined plane of inclination 60° with velocity of 20 ms⁻¹ and stops after 2.00 s. If g=10 ms⁻², then the approximate value of coefficient of friction is

A body with mass 5 kg is acted upon a force F=(-3i+4j) N. If its initial velocity at t=0 is v=(6i-12j)m/s. The time at which it will just have a velocity along the y-axis is

A marble block of mass 2 kg lying on ice when given a velocity of 6 m/s is stopped by friction in 10 s. Then the coefficient of friction is

You are marooned on a frictionless horizontal plane and cannot exert any horizontal force by pushing against the surface. How can you get off

A particle of mass 100 g tied to a string is rotated along a circle of radius 0.5 m. The breaking tension of string is 10 N. The maximum speed with which particle can be rotated without breaking the string is

A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min.The coefficient of friction between the wall and his clothing is 0.15.When the floor is suddenly removed, what is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall without falling (approximately)?

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone?

A road of width 20m forms an arc of radius 15m, its outer edge is 2m higher than its inner edge. For what velocity the road is banked?

A ball moving with velocity 2 ms⁻¹ collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5, then their velocities (in ms⁻¹) after collision will be

The minimum velocity (in ms⁻¹) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is :

A stone of mass 1kg is tied to a string 4m long and is rotated at constant speed of 40 ms⁻¹ in a vertical circle. The ratio of the tension at the top and the bottom is (take ,g = 10ms⁻² )

For a particle in a non-uniform accelerated circular motion correct statement is

A boy whirls a stone in a horizontal circle of radius 1.5 m and at height 2.0 m above level ground. The string breaks and the stone flies off tangentially and strikes the ground after travelling a horizontal distance of 10 m. What is the magnitude of the centripetal acceleration of the stone while in circular motion?

A coin placed on a rotating turn table just slips,if it is placed at a distance of 8 cm from the centre.  If angular velocity of the turn table is doubled, it will just slip at a distance of

An aircraft executes a horizontal loop of radius 1 km with a speed of 900 kmh⁻¹. Ratio of centripetal acceleration to acceleration due to gravity is

Two blocks of masses m₁=4 kg and m₂=2 kg are connected to the ends of a string which passes over a massless, frictionless pulley. The total downward thrust on the pulley is nearly

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A bob is suspended from the roof of the car by a light wire of length 1.0 m. The angle made by the wire with the vertical is

Find the maximum velocity with which a train can be moved on a circular track of radius 200 m. The banking of the track is 5.71°(Given, tan 5.71°= 0.1)

A body of mass M hits normally a rigid wall with velocity V and bounces back with the same velocity. The impulse experienced by the body is

A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.5 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

When a ceiling fan is switched off its angular velocity reduces to 50% while it makes 36 rotations. How many more rotation will it make before coming to rest? (assume uniform angular retardation)

A body is hanging from a rigid support by an inextensible string of length l. It is struck inelastically by an identical, body of mass m with horizontal velocity v=√2g l, the tensions in the string increases just after striking by

A disc of mass 100 g is kept floating horizontally in air by firing bullets, each of mass 5g with the same velocity at the same rate of 10 bullets/s. The bullets rebound with the same speed in opposite direction, the velocity of each bullet at the time of impact is

The string of a pendulum is horizontal. The mass of bob attached to it is m. Now, the string is released. The tension in the string in the lowest position is

A motorcycle moving with a velocity 72 kmh⁻¹ on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 m,the acceleration due to gravity is 10 ms⁻².In order to avoid skidding, he must not bent with respect to the vertical plane by an angle greater than

A heavy stone hanging from a massless string of length 15 m is projected horizontally with speed 147 ms⁻¹. The speed of the particle at the point where the tension in the string equals the weight of the particle is

A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

An open knife edge of mass 200 g is dropped from height 5 m on a cardboard. If the knife edge penetrates distance 2m into the cardboard, the average resistance offered by the cardboard to the knife edge is

Two wheels having radii in the ratio 1:3 are connected by a common belt. If the smaller wheel is accelerated from rest at a rate 1.5 rad s⁻² for 10 s.the velocity of bigger wheel is

A car wheel is rotated to uniform angular acceleration about its axis .Initially its angular velocity is zero. It rotates through an angle θ₁ in the first 2s, in the next 2s,it rotates through an additional angle θ₂, the ratio of θ₂/θ₁ is

A 0.5 kg ball moving with a speed of 12 ms⁻¹ strikes a hard wall at an angle of 30ᵒ with the wall.It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for 0.25 s, the average force acting on the wall is

Four blocks of same mass connected by cords are pulled by a force F on a smooth horizontal surface, as shown in the figure. The tensions T₁,T₂ and T₃ will be

In the diagram shown in figure,match the following (take, g=10 m/s²)
Column I Column II
A. Acceleration of 2kg block 1.8 SI unit
B. Net force on 3 kg block 2.25 SI unit
C. Normal reaction between 2 kg and 1 kg 3.2 SI unit
D. Normal reaction between 3 kg and 2 kg 4.45 SI unit
5. None

A body of mass 2 kg travels according to the law x(t)=pt+qt²+rt³, where p=3 m/s, q=4 m/s² and r=5 m/s³. The force acting on the body at t=2 s is

A car of mass m is moving on a level circular track of radius R. If µ(s) represents the static friction between the road and tyres of the car, the maximum speed of the car in circular motion is given by :

A block of mass m is moving on a wedge with the acceleration aᵒ. The wedge is moving with the acceleration a₁. The observer is situated on wedge. The magnitude of pseudo force on the block is

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally, so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is accelerated due to gravity) will be

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0 m/s². If g = 10 ms⁻², the tension in the supporting cable is

Three solids of masses m₁,m₂ and m₃ are connected with weightless string in succession and are placed on a frictionless table. If the mass m₃ is dragged with a force, the tension(T) in the string between m₂ and m₃ is

A circular road of radius 1000 m has banking angle 45°.The maximum safe speed of a car having mass 200 kg will be, if the coefficient of the friction between the tyre and road is 0.5