Second Law of Motion

Q.

A rope which can withstand a maximum tension of 400 N is hanging from a tree. If a monkey of mass 30 kg climbs up the rope, in which of the following cases will the rope break? Take $g=10m{s}^{-2}$ and neglect the mass of the rope.

1. The monkey climbs up with a uniform speed of $5m{s}^{-1}$.

2. The monkey climbs up with a uniform acceleration of $2m{s}^{-2}$.

3. The monkey climbs up with a uniform acceleration of $5m{s}^{-2}$.

4. The monkey climbs down with a uniform acceleration of $5m{s}^{-2}$.

Q. For the system shown in the figure, the pulley is smooth and massless, the string is massless and inextensible. If the acceleration of the system is ($a$) then, find out the ratio of tensions $T_1$ and $T_2$.
(Take $g=10{\text{m/s}}^2)$

1. $20:3$
   
2. $5:1$
   
3. $3:1$
   
4. $5:2$
   

Q. The force exerted on $5\text{kg}$ block by $10\text{kg}$ block placed in the lift, shown in the figure is

Q. A gas of density $\rho$ flows with velocity $v$ along a pipe of cross - sectional area $S$ and bent to an angle of ${90}^{\circ }$ at point $A$. What force does the gas exert on the pipe at point $A$ ?

1. $\sqrt{5}S{v}^2\rho$
2. $\sqrt{2}S{v}^2\rho$
3. $\sqrt{7}S{v}^2\rho$
4. $\sqrt{3}S{v}^2\rho$

Q. Two-point charges $Q_1$ and $Q_2$ are $3\text{m}$ apart and their combined charge is $20\mu \text{C}$. If one repels the other with force of $0.075\text{N}$. Calculate the two charges. (in $\mu \text{C}$)

1. $10,10$
2. $15,5$
3. $35,-15$
4. $25,-5$

Q. A $20\text{kg}$ monkey slides down a vertical rope with a constant acceleration of $7{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, what is the tension in the rope ?

1. $140\text{N}$
2. $100\text{N}$
3. $60\text{N}$
4. $30\text{N}$

Q. A body of mass $1kg$ is moving with a velocity $v=10\hat{i}+5\hat{j}$ m/s. What is the angle made by the momentum vector with $x-$ axis?

1. ${\tan }^{-1}\frac{5}{2}$
2. ${\tan }^{-1}\frac{1}{4}$
3. ${\tan }^{-1}\frac{1}{2}$
4. ${\tan }^{-1}\frac{3}{2}$

Q. A water jet, whose cross sectional area is ${}^{\prime }{a}^{\prime }$ strikes a wall making an angle ${}^{\prime }\theta {}^{\prime }$ with the normal and rebounds elastically. The velocity of water of density ${}^{\prime }{d}^{\prime }$ is $V$.
Force exerted on wall is

1. $2a{V}^{2}d\cos \theta$
2. $2a{V}^{2}d\sin \theta$
3. $2aVd\cos \theta$
4. $aVdcos\theta$

Q. A force $F$ is applied horizontally on mass $m_1$ as shown in figure. Find the contact force between $m_1$ and $m_2$.

1. $\frac{m_{2}F}{m_1+m_2}$
2. $\frac{m_{1}F}{m_1+m_2}$
3. $m_{1}F$
4. $m_{2}F$

Q. A particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t=0$, a force $F=kt$ ($k$ is a constant) acts along the direction of motion of particle for the time interval $T$ so that its momentum changes from $p$ to $5p$. The value of $T$ is

1. $\sqrt{\frac{2p}{k}}$
2. $2\sqrt{\frac{p}{k}}$
3. $2\sqrt{\frac{2p}{k}}$
4. $2\sqrt{\frac{k}{p}}$

Q. Consider the system shown in figure. System is released from rest, find the tension (in Newton) in the cord connected between 1 kg and 2 kg blocks. $(g=10\frac{m}{s^2})$

Q.

Two masses m and 2m are joined to each other by means of a frictionless pulley as shown below. When the mass 2m is released, the mass m will ascend with an acceleration of

1. $\frac{g}{3}$

2. $\frac{g}{2}$

3. $g$

4. $2g$

Q.

A force F is applied horizontally to a block A of mass $m_1$ which is in contact with a block B of mass $m_2$, as shown in the figure. If the surfaces are frictionless, the force exerted by A on B is equal to

1. $\frac{m_{1}F}{m_2}$

2. $\frac{m_{2}F}{m_1}$

3. $\frac{m_{1}F}{m_1+m_2}$

4. $\frac{m_{2}F}{m_1+m_2}$

Q. In the figure, all pulleys are massless and strings are light.
$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) 1 kg block}& \text{(p)}\text{will remain stationary}\\ \text{(b) 2 kg block}& \text{(q)}\text{will move down}\\ \text{(c) 3 kg block}& \text{(r)}\text{will move up}\\ \text{(a) 4 kg block}& \text{(s)}5{\text{m/s}}^2\\ & \text{(t)}10{\text{m/s}}^2\end{array}$

1. $a-t,b-p,c-s,d-q$
2. $a-p,b-t,c-s,d-q$
3. $a-r,t,b-p,c-q,d-q,s$
4. $a-r,b-p,c-q,d-p$

Q. A particle of mass $2\text{kg}$ moves with an initial velocity of $(4\hat{i}+2\hat{j}){\text{ms}}^{-1}$ on the x - y plane. A force $\overrightarrow{F}=(2\hat{i}-8\hat{j})\text{N}$ acts on the particle. The initial position of the particle is $(2,3)\text{m}$. Then when particle reaches $y=3\text{m},$

1. Possible value of $x$ is only $x=2\text{m}$
2. Possible value of $x$ is not only $x=2\text{m}$, but there exists some other value of $x$ also
3. Time taken is $2\text{s}$
4. All of the above

Q. A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ${\omega }_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega \left(t\right)$ will vary with time $t$ as

1. 
2. 
3. 
4. 

Q.

A mass m is suspended from a rigid support P by means of a massless string as shown in the figure. A horizontal force F is applied at point O of the rope. The system is in equilibrium when the string makes an angle $\theta$ with the vertical. Then the relation between tension T, force F and angle $\theta$ is

1. $F=Tsin\theta$

2. $F=Tcos\theta$

3. $F=\frac{T}{sin\theta }$

4. $F=\frac{T}{cos\theta }$

Q.

On forgetting his 25th anniversary, Vijay as a present from his wife, receives a shoe of 0.5 kg thrown at him with 10 m/s velocity. Find the momentum of assault.

1. 10 Kg m/s

2. 5 N

3. 0.5 N

4. 5 kg m/s

Q. A monkey of mass $20\text{kg}$ is holding a vertical rope. The rope will not break when a mass of $25\text{kg}$ is suspended from it but will break if the mass exceeds $25\text{kg}$. What is the maximum acceleration with which the monkey can climb up along the rope? ($g=10{\text{m/s}}^2)$

1. $5{\text{m/s}}^2$
2. $10{\text{m/s}}^2$
3. $25{\text{m/s}}^2$
4. $2.5{\text{m/s}}^2$

Q. A player caught a cricket ball of mass 150 g moving at a rate of 20 m/s.If he catches it in 0.1 s, force of the blow exerted by ball on the player is.

1. 300 N
2. 30 N
3. 150 N
4. 3 N

Q. Paragraph for below question
नीचे दिए गए प्रश्न के लिए अनुच्छेद

A disc (M, R) rolling without slippage on a rough horizontal surface with coefficient of friction μ collides with smooth wall elastically.

किसी खुरदरे क्षैतिज पृष्ठ जिसका घर्षण गुणांक μ है, पर बिना फिसले लुढ़क रही एक डिस्क (M, R) चिकनी दीवार से प्रत्यास्थ रूप से टकराती है।

Q. Velocity of top-most point of disc just after collision, is

प्रश्न - टक्कर के ठीक बाद डिस्क के शीर्षतम बिन्दु का वेग है

1. Zero
   शून्य
2. 2v₀
3. $\frac{v_0}{2}$
4. v₀

Q.

Two blocks of mass 2 kg and 4 kg are kept in contact with each other on a smooth horizontal surface. A horizontal force of 12 N is applied on the first block due to which they move with certain constant acceleration. Calculate the force between the blocks.

1. 2 N

2. 4 N

3. 8 N

4. 16 N

Q. A water pipe has an internal diameter of $10\text{cm}$. Water flows it at the rate of $20\text{m/sec}$. The water jet strikes normally on a wall and falls dead. Find the force( in N upto two decimal places) on the wall.(Assume $\pi =3.14$)

Q.

If the force on a rocket moving with a velocity of 300 m/s is 210 N, then the rate of combustion of the fuel is

1. 0.7 kg/s

2. 1.4 kg/s

3. 0.07 kg/s

4. 10.7 kg/s

Q. An impulse acts on a body of constant mass$\left(m\right)$ initially at rest. If it travels with constant velocity afterwards, which graph represents the variation of force$\left(F\right)$ with time during the time impulse was acting.

1. 
2. 
3. 
4. 

Q.

A man of mass M is standing on a plank kept in a box. The plank and box as a whole has mass m. A light string passing over a fixed smooth pulley connects the man and box. If the box remains stationary, find the tension in the string and the force exerted by the man on the plank.

1. $\frac{(m+M)g}{2},\frac{(M-m)g}{2}$

2. $(m+M)g,\frac{(M-m)g}{2}$

3. $\frac{(m+M)g}{2},(M-m)g$

4. $(m+M)g,(M-m)g$

Q. The initial speed of a body of mass $2.0\text{kg}$ is $5.0{\text{ms}}^{-1}$. A force acts for 4 seconds in the direction of motion of the body. The force-time graph is shown in figure. Calculate the impulse of the force and also the final speed of the body.

1. $8.50\text{N s},9.25{\text{ms}}^{-1}$
2. $4.25\text{N s},9.25{\text{ms}}^{-1}$
3. $4.25\text{N s},4.25{\text{ms}}^{-1}$
4. $8.50\text{N s},4.25{\text{ms}}^{-1}$

Q.

A block of mass M is pulled along a horizontal frictionless suface by a rope of mass m. If a force F is applied at the free end of the rope, the net force exerted on the block will be

1. $\frac{FM}{(M+m)}$

2. $\frac{Fm}{(M+m)}$

3. $\frac{FM}{(M-m)}$

4. $F$

Q. Paragraph for below question
नीचे दिए गए प्रश्न के लिए अनुच्छेद

A disc (M, R) rolling without slippage on a rough horizontal surface with coefficient of friction μ collides with smooth wall elastically.

किसी खुरदरे क्षैतिज पृष्ठ जिसका घर्षण गुणांक μ है, पर बिना फिसले लुढ़क रही एक डिस्क (M, R) चिकनी दीवार से प्रत्यास्थ रूप से टकराती है।

Q. Just after the collision, velocity of point of disc in contact with floor, is

प्रश्न - टक्कर के ठीक बाद, डिस्क के उस बिन्दु, जो फर्श के साथ सम्पर्क में है, का वेग है

1. $\frac{v_0}{2}$
2. $\frac{3v_0}{2}$
3. 2v₀
4. $\frac{5v_0}{2}$

Q. A hot air balloon, released from ground, moves up with a constant acceleration of $5{\text{ms}}^{-2}$. A stone is released from it at the end of $8s$. Find the height (in$\text{m}$) of the stone from the ground, $8s$ after it is released from the balloon. (Take $g=10{\text{ms}}^{-2}$)