Laws of Motion

A car travels on a circular racetrack of radius 50 m , which is banked at an angle $\theta$. If the car travels at a speed $10 \mathrm{~ms}^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be ...

A box of mass 15 kg is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is 0.12 . Keeping the box in stationary state over the trolley, the maximum acceleration with which the tro...

The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it, are respectively:

There are two inclined surfaces of equal length $(L)$ and same angle of inclination $45^{\circ}$ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough sur...

A box of mass \(5 \mathrm{~kg}\) is pulled by a cord, up along a frictionless plane inclined at \(30^{\circ}\) with the horizontal. The tension in the cord is \(30 \mathrm{~N}\). The acceleration of the box is (Take $$g=10 \mathrm{~m} \math...

A horizontal force \(10 \mathrm{~N}\) is applied to a block \(A\) as shown in figure. The mass of blocks \(A\) and \(B\) are \(2 \mathrm{~kg}\) and 3 \(\mathrm{kg}\) respectively. The blocks slide over a frictionless surface. The force exer...

A particle moving with uniform speed in a circular path maintains:

A block of mass 2 kg is placed on inclined rough surface AC (as shown in figure) of coefficient of friction \(\mu\). If g = 10 m s\(^{-2}\), the net force (in N) on the block will be:

A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels \(24 \mathrm{~cm}\) through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates ...

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15
\(\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)\)...

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is :

In the diagram shown, the normal reaction force between 2 kg and 1 kg is (Consider the surface, to be smooth) :
(Given g = 10 ms\(-\)2)

If \(\overrightarrow F = 2\widehat i + \widehat j - \widehat k\) and \(\overrightarrow r = 3\widehat i + 2\widehat j - 2\widehat k\), then the scalar and vector products of \(\overrightarrow F\) and \(\overrightarrow r\) have the magnit...

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is :

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when :

A block of mass 10 kg is in contact against the inner wall of a hollow cylindrical drum of radius 1 m. The coefficient of friction between the block and the inner wall of the cylinder is 0.1. The minimum angular velocity needed for the cyli...

A block of mass m is placed on a smooth inclined
wedge ABC of inclination q as shown in the
figure. The wedge is given an acceleration ‘a’
towards the right. The relation between a and q
for the block to remain stationary on the wedge
is

Which one of the following statements is
incorrect?

One end of string of length \(l\) is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed '\(\upsilon\)', the net force on the particle ...

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the s...

A car is negotiating a curved road of radius R. The road is banked at an angle \(\theta\). The coefficient of friction between the tyres of the car and the road is \(\mu\)s. The maximum safe velocity on this road is

A block A of mass m1 rests on a horizontal table. A light string connected to it passes over a frictionless pully at the edge of table and from its other end another block B of mass m2 is suspended. The coefficient of kinetic friction betwe...

Three blocks A, B and C, of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block, then the contact force between A and B is

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius \({r \over 2}\) and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they expr...

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30o, the box starts to slip and slides 4.0 m down the plank in 4.0 s.

The coefficients of static and kinet...

A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a ?

A system consists of three masses m1, m2 and m3 connected by a string passing over a pulley P. The mass m1 hangs freely and m2 and m3 are on a rough horizontal table (the coefficient of friction = \(\mu\)). The pulley is frictionless and o...

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

The upper half of an inclined plane of inclination \(\theta\) is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between t...

Three blocks with masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upwards at constant speed v. What is the net force on the block of mass 2m ? (g is the ac...

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

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 conveyor belt is moving at a constant speed of 2 ms\(-\)1. A box is gently dropped on it. The coefficient of friction between them is \(\mu\) = 0.5. The distance that the box will move relativce to belt before coming to rest on it, takin...

A block of mass m is in contact with the cart C as shown in the figure.
The coefficient of static friction between the block and the cart is \(\mu\). The acceleration \(\alpha\) of the cart that will prevent the block from falling satisfi...

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

A body, under the action of a force \(\overrightarrow F = 6\widehat i - 8\widehat j + 10\widehat k,\) acquires an accelerations of 1 m/s2. The mass of this body must be

Three forces acting on a body are shown in the figure. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

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

A roller coaster is designed such that riders experience ''weightlessness'' as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between

A block B is pushed momentarily along a horizontaly surface with an initial velocity V. If  \(\mu\)  is the coefficient of sliding friction between B and the surface, block B will come to rest after a time

A block of mass m is placed on a smooth wedge of inclination \(\theta\). 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 will be (g is acceleration due...

The coefficient of static friction, \(\mu\)s, between block A of mass 2 kg and the table as shown in the figure is 0.2. What would be the maximum mass value of block B so that the two blocks do not move? The string and the pulley are assu...

A monkey of mass 20 kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the ro...

A man weight 80 kg. He stands on a weighting scale in a lift which is moving upwards with a uniform acceleration of 5 m/s2. What would be the reading on the scale ? (g = 10 m/s2)

A block of mass 10 kg placed on rough horizontal surface having coefficient of friction m = 0.5, if a horizontal force of 100 N acting on it then acceleration of the block will be

A lift of mass 1000 kg which is moving with acceleration of 1 m/s2 in upward direction, then the tension developed in string which is connected to lift is

An object of mass 3 kg is at rest. Now a force of \(\overrightarrow F\) = 6t2 \(\widehat i\) + 4t \(\widehat j\) is applied on the object then velocity of object at t = 3 sec. is

250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m then the load is lifted to 3 m. the efficiency of pulley system will be

A 1 kg stationary bomb is exploted in three parts having mass 1 : 1 : 3 respectively. Parts having same mass move in perpendicular direction with velocity 30 m/s, then the velocity of bigger part will be