Laws of Motion PYQs

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 trolley can be moved horizontally in m s⁻² is: (g = 10 m/s²)

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° 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 surface than on the smooth surface. The coefficient of kinetic friction (μk) between the object and the rough surface is close to

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of 60° with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (g = 10 m/s²)

A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes:

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity v₁ while body B is at rest before collision. The velocity of the system after collision is v₂. The ratio v₁ : v₂ is:

A horizontal force 10 N is applied to a block A as shown in figure. The mass of blocks A and B are 2 kg and 3 kg, respectively. The blocks slide over a frictionless surface. The force exerted by block A on block B is:

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 :

A bullet from a gun is fired on a rectangular wooden block with velocity $u$. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes $\frac{u}{3}$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is:

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 (g = 10 m s⁻²).

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed v, the speed of the third (lighter) fragment is:

A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is (g = 10 m/s²) nearly

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 gravity (g) is:

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time t₁ if the elevator is at rest and in time t₂ if the elevator is moving uniformly. Then:

A truck is stationary and has a bob suspended by a light string, in a frame attached to the truck. The truck suddenly moves to the right with an acceleration of a. The pendulum will tilt

An object flying in air with velocity $\left(20\hat{i}+25\hat{j}-12\hat{k}\right)$ suddenly breaks into two pieces whose masses are in the ratio $1:5$. The smaller mass flies off with a velocity $\left(100\hat{i}+35\hat{j}+8\hat{k}\right)$. The velocity of the larger piece will be:

A body of mass $m$ is kept on a rough horizontal surface (coefficient of friction $= \mu$). A horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given by $F$, where $F$ is

A particle of mass $5m$ at rest suddenly breaks on its own into three fragments. Two fragments of mass $m$ each move along mutually perpendicular directions with speed $v$ each. The energy released during the process is:

Which one of the following statements is incorrect?

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

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 string is cut, are respectively

One end of a 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 a circle with speed $v$, the net force on the particle directed towards the centre will be ($T$ represents the tension in the string):

A rigid ball of mass $m$ strikes a rigid wall at $60^\circ$ and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be:

Two identical balls $A$ and $B$ having velocities of $0.5\ \text{m/s}$ and $-0.3\ \text{m/s}$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

Two particles A and B move with constant velocities $\vec{u}_1$ and $\vec{u}_2$. At the initial moment their position vectors are $\vec{r}_1$ and $\vec{r}_2$ respectively. The condition for particles A and B to collide is:

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 $30^\circ$, the box starts to slip and slides $4.0\,\text{m}$ down the plank in $4.0\,\text{s}$. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

A system consists of three masses $m_1$, $m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction = $\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is: Assume $m_1 = m_2 = m_3 = m$.

The force 'F' acting on a particle of mass 'm' is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is :

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 body of mass (4m) is lying in the x-y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m), move perpendicular to each other with equal speeds (v). The total kinetic energy generated due to explosion is:

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 upward at constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1\,\mathrm{kg}$ moves with a speed of $12\,\mathrm{m\,s^{-1}}$ and the second part of mass $2\,\mathrm{kg}$ moves with $8\,\mathrm{m\,s^{-1}}$ speed. If the third part flies off with $4\,\mathrm{m\,s^{-1}}$ speed, then its mass is:

A car of mass m is moving on a level circular track of radius R. If $\mu_s$ 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 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 previous height, the momentum when it hits the ground will change by:

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 mass m moving horizontally along the x-axis with velocity v collides and sticks to a mass 3m moving vertically upward along the y-axis with velocity 2v. The final velocity of the combination is:

The mass of lift is $2000\,\mathrm{kg}$. When the tension in the supporting cable is $28000\,\mathrm{N}$, then its acceleration is:

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are: a $1\,\mathrm{kg}$ first part moving with a velocity of $12\,\mathrm{m\,s^{-1}}$ and a $2\,\mathrm{kg}$ second part moving with a velocity of $8\,\mathrm{m\,s^{-1}}$. If the third part flies off with a velocity of $4\,\mathrm{m\,s^{-1}}$, its mass would be:

A body under the action of a force $\vec{F}=6\hat{i}-8\hat{j}+10\hat{k}$ acquires an acceleration of $1\,\mathrm{m\,s^{-2}}$. The mass of the body must be:

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

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

A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

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 body of mass 3 kg is under a constant force which causes a displacement s in metres given by the relation s = (1/3)t², where t is in seconds. Work done by the force in 2 s is:

A 0.5 kg ball moving with a speed of 12 m/s strikes a hard wall at an angle of 30° 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: