Newton's Second Law

Q.

A train starts from a station and and moves with constant acceleration for 2 minutes. If is covers a distance of 400 m in this period find the acceleration.

Q. If mass of $A=10\text{kg}$ , coefficient of static friction= $0.2$, coefficient of kinetic friction = $0.2$. The mass of $B$ is $20\text{kg}$. Find acceleration of masses

1. $6{\text{m/s}}^2$
2. $7{\text{m/s}}^2$
3. $8{\text{m/s}}^2$
4. $9{\text{m/s}}^2$

Q.

A block moving on a surface with a velocity of $20m{s}^{-1}$ comes to rest because of surface friction over a distance of $40m$. The coefficient of dynamic friction is (take, $g=10m{s}^{-2}$)

1. $0.5$

2. $0.3$

3. $0.2$

4. $0.1$

Q. A block is kept on a smooth inclined plane of angle of inclination ${30}^{\circ }$ that moves with a constant acceleration so that the block does to slide relative to the inclined plane.
Let $F_1$ be the contact force between the block and the plane. Now the inclined plane stops, then let $F_2$ be the contact force between the block and the plane. The value of $\frac{F_1}{F_2}$ is

1. $1$
2. $\frac{4}{3}$
   
3. $2$
4. $\frac{3}{2}$
   

Q. Two blocks are connected over a massless pulley as shown in the figure. The mass of block $A$ is $10\text{kg}$ and coefficient of kinetic friction is $0.2$. Block $A$ slides down the incline at constant speed. The mass of the block $B$ (in $\text{kg}$) is

1. $5.4$
2. $3.3$
3. $4.2$
4. $6.8$

Q. A car having a mass of $1000\text{kg}$ is moving at a speed of $30\text{m/s}$ . Brakes are applied to bring the car to rest. If the frictional force between the tyres and the road surface is $5000\text{N}$ , the car will come to rest in

1. $10\text{s}$
2. $12\text{s}$
3. $5\text{s}$
4. $6\text{s}$

Q.

A fireman of mass 80 kg slides down a pole during a rescue mission. The force of friction is constant at 720 N. Find the acceleration of the man.

Q.

The acceleration of a particle is given by the a = x where x is a constant. If the particle starts at origin from rest, its distance from origin after time t is given by

1. $\frac{x{t}^2}{2}$

2. $\frac{x^2{t}^2}{2}$

3. $\frac{x^3{t}^3}{6}$

4. $\frac{\sqrt{x}{t}^2}{2}$

Q.

A truck and a car moving with the same kinetic energy are brought to rest by the application of brakes which provides equal retarding forces. Which of them will come to rest in a shorter distance?

1. The truck

2. The car

3. Both will travel the same distance before coming to rest

4. Cannot be predicted

Q. A child weighing $25\text{kg}$ slides down the rope hanging from a branch of a tall tree. If force of friction acting against him is $200\text{N}$, the acceleration of child is (take $g=10{\text{m/s}}^2$ )

1. $8{\text{m/s}}^2$
2. $5{\text{m/s}}^2$
3. $2{\text{m/s}}^2$
4. $22.5{\text{m/s}}^2$

Q.

A body of mass $60kg$ is dragged with just enough force to start moving on a rough surface with coefficients of static and kinetic frictions $0.5$ and $0.4$ respectively. On applying the same force, what is the acceleration?

1. $0.98m{s}^{-2}$

2. $9.8m{s}^{-2}$

3. $0.54m{s}^{-2}$

4. $5.292m{s}^{-2}$

Q. A block of mass 10 kg is placed on a rough horizontal surface having coefficient of friction 3. Find minimum force required to move the block- 1) 503 2) 3 3)53 4)100

Q. A block of mass $1\text{kg}$ is placed on a rough incline as shown. The coefficient of friction between block and incline is $0.4$. The acceleration of block is $[g=10{\text{ms}}^{-2},\sqrt{3}=1.7]$

1. Zero
2. $5{\text{ms}}^{-2}$
3. $1.6{\text{ms}}^{-2}$
4. $6.5{\text{ms}}^{-2}$

Q.

What happens to inertia when velocity is doubled?

Q. In the figure below, a block of weight 60 N is placed on a rough surface. The coefficient of friction between the block and the surface is 0.5. What should be the weight W such that
the block does not slip on the surface?

1. $\frac{60}{\sqrt{2}}N$
2. $60N$
3. $30N$
4. $\frac{30}{\sqrt{2}}N$

Q.

A metre stick weighing 240 g is pivoted at its upped end in such a way that it can freely rotate in a vertical plane through this end (figure 10-E12). A particle of mass 100 g is attached to the upped end of the stick through a light string of length 1 m. Initially, the rod is kept vertical and the string horizontal when the system is released from rest. The particle collides with the lower end of the stick and sticks there. Find the maximum angle through which the stick will rise.

Q. A fireman of mass $60kg$ slides down a pole. He is pressing the pole with a force of $600N$. The coefficient of friction between the hands and the pole is $0.5$, with what acceleration will the fireman slide down $(g=10m/s^2)$

1. $2.5m/s^2$
2. $1m/s^2$
3. $10m/s^2$
4. $5m/s^2$

Q.

A body is coming with a velocity of $72km/h$ on a rough horizontal surface with a coefficient of friction of $0.5$. If the acceleration due to gravity is $10m{s}^{-2}$, find the minimum distance, it can be stopped.

1. $400m$

2. $40m$

3. $0.40m$

4. $4m$

Q.

A ball moving with a momentum of 15kgm/s, strikes against a wall at an angle of 30° and is deflected back with the same momentum at the same angle. Calculate the impulse.

Q. In the arrangement shown, the rod is freely pivoted at point O and is in contact with the equilateral triangular block which can move on the horizontal frictionless ground. As the block is given a speed $v$ in the forward direction, the rod rotates about point O. Find the angular velocity of the rod in rad/s at the instant when $\theta ={30}^{\circ }$. [Take $v=20\text{m/s}$, $a=1\text{m}$]

Q. Find out the distance travelled by the block on incline before it stops. Initial velocity of the block is $10\text{m/s}$ and co-efficient of friction between the block and incline is $\mu =0.5$.
$(\text{Take}g=10{\text{m/s}}^2)$

1. $\text{5 m}$
2. $\text{4 m}$
3. $\text{6 m}$
4. $\text{10 m}$

Q.

A plank of mass 10 kg rests on a smooth horizontal surface.Two blocks A and B of masses m_a = 2 kg and m_b =1 kg lies at a distance of 3 m on the plank. The friction coefficient between the blocks and plank are f_a=0.3 and f_b=0.1.Now a force F=15 N is applied to the plank in horizontal direction.Find the time (in sec) after which block A collides with B.

Q. Two balls of masses $m_1$ and $m_2$ are moving towards each other with speeds $u_1$ and $u_2$ respectively. After they collide head–on, their speeds are $v_1$ and $v_2$ respectively. (Take $m_1=8\text{kg},m_2=2\text{kg},u_2=3\text{m/s}$) All quantities are in SI units and $e$ is the coefficient of restitution.
Match the statements in List $1$ with results in List $2$
$\begin{array}{cc}\text{List 1}& \text{List 2}\\ \text{A) The speed}{u}_1\text{so that both the balls are moving in the same direction after collision is (}e=0.5)& \text{p)}1/14\\ \text{B) The speed}{u}_1\text{so that maximum fraction of energy is transferred to mass}{m}_2\text{(Assume}e=1\text{) is}& \text{q)}1.5\\ \text{C) If}{u}_1=0.5m/s\text{and}{m}_2\text{stops, then the value of e is}& \text{r)}2\\ \text{D) If}{u}_1=3m/s\text{and e=0,}\text{then fractional loss of KE after collision is}& \text{s)}0.64\end{array}$

1. $A–r,q,B–q,C–p,D–p$
2. $A–r,B–q,C–p,D–s$
3. $A–r,p,B–p,C–q,D–s$
4. $A–q,r,B–r,C–p,D–s$

Q. A particle is projected up a large inclined plane from a point $O$ as shown in the figure. The projection velocity has a magnitude of $5.5m{s}^{-1}$ and its direction makes an angle ${37}^{\circ }$ with the inclined plane. The inclination of the plane is also ${37}^{\circ }$. The inclined plane starts moving towards left with an acceleration $a_0=5m{s}^{-2}$ at the moment the particle is projected. If the particle strikes the inclined plane at a point $P$, choose the correct statements.

1. The time taken by the particle to move from $O$ to $P$ is $0.6s$
2. The time taken by the particle to move from $O$ to $P$ is $0.4s$
3. The displacement of the particle w.r.t. the inclined plane is $2.56m$
4. The displacement of the particle w.r.t. the inclined plane is $2.28m$

Q. Two boats were going downstream with different velocities. When one overtook the other, a plastic ball was dropped from one of the boats. Sometime later, both boats turned back simultaneously and went at the same speeds as before (relative to the river) towards the spot where the ball had been dropped. Which boat will reach the ball first?

1. The boat which has greater velocity (relative to river).
2. The boat which has lesser velocity (relative to river).
3. Both will reach the ball simultaneously.
4. Cannot be decided unless we know the actual values of the velocities and the time after which they turned around.

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

1. 10 m/s${}^2$
2. 5 m/s${}^2$
3. 15 m/s${}^2$
4. 0.5 m/s${}^2$

Q. Two bodies of equal masses are connected by a light inextensible string passing over a smooth frictionless pulley. The percent of mass that should be transferred from one to another, so that both the masses move $50\text{m}$ in $5\text{s}$ is

1. $30\%$
2. $40\%$
3. $70\%$
4. $50\%$

Q. A $4\text{kg}$ block is placed on top of a long $12\text{kg}$ block, which is accelerating along a smooth horizontal table at $a=5.2\text{m}/{\text{s}}^2$ under application of an external constant force. let minimum co-efficient of friction between the two blocks which will prevent the $4\text{kg}$ block from sliding is $\mu$ and co-efficient of friction between the blocks is only half of this minimum value i.e., $\frac{\mu }{2}$. Find the amount of heat generated due to sliding between the two blocks during the time in which $12\text{kg}$ block moves $10\text{m}$ starting from rest.

1. $32\text{J}$
2. $42\text{J}$
3. $52\text{J}$
4. $62\text{J}$

Q.

In the shown figure $m_A,m_{B}and{m}_C$ are the masses of the three blocks, the incline is frictionless $m_A=5kg,m_B=10kg,m_C=2kg$. coefficient of friction between A and B is 0.5 and between B and C is 0.1 (Take g = 10 $m/s^2$) On the basis of above data answer the following questions.

What is the frictional force on block A

1. 30 N

2. 48 N

3. 78 N

4. 18 N

Q. A $60kg$ body is pushed with just enough force to start it moving across a floor and the same force continues to act afterwards. The coefficients of static friction and sliding friction are $0.5$ and $0.4$ respectively. The acceleration of the body is
(Take $g=10m/s^2$)

1. $6m/s^2$
2. $4.9m/s^2$
3. $3.92m/s^2$
4. $1m/s^2$