Problem Solving

Q.

A weightless ladder, 20 ft long rests against a frictionless wall at an angle of 60⁰ with the horizontal. A 150 pound main is 4 ft from the top of the ladder. A horizontal force is needed to prevent it from slipping choose the correct magnitude from the following

1. 175 lb

2. 100 lb

3. 70 lb

4. 150 lb

Q.

What is the difference between Thrust and Force?

Q. In the figure shown, if the velocity of end A is $v_0$, find the velocity of the end $B$ of the rigid rod at the given instant.

1. $\frac{v_0}{\sqrt{3}}$
2. $\frac{2v_0}{\sqrt{3}}$
3. $v_0\sqrt{\frac{2}{3}}$
4. $\frac{v_0}{\sqrt{2}}$

Q. Find the height by which the sphere rises when the wedge touches the wall. Let the initial distance between the wedge and the wall is $10\text{m}$ and the wedge is moved to the left until it touches the wall. (Assume all surfaces to be smooth)

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

Q. A painter of mass $100\text{kg}$ is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is $450\text{N}$. If the crate weighs $25\text{kg}$ then, find the acceleration of the system and the tension in the rope.

1. $2{\text{ms}}^{-2},750\text{N}$
2. $3{\text{ms}}^{-2},500\text{N}$
3. $4{\text{ms}}^{-2},570\text{N}$
4. $1{\text{ms}}^{-2},50\text{N}$

Q.
Find the acceleration of $B$ if the acceleration of $A$ is $4m/s^2$ . ($B$ is only allowed to move in vertical direction)

1. $\frac{2}{\sqrt{3}}m/s^2$
2. $\frac{4}{\sqrt{3}}m/s^2$
3. $2\sqrt{3}m/s^2$
4. $4\sqrt{3}m/s^2$

Q. Find $\overrightarrow{a}$ of the 4 kg block:

1. 1 $m/s^2$
2. 4 $m/s^2$
3. 8 $m/s^2$
4. 2 $m/s^2$

Q. Find the tension (in $N$) in the string connecting the $2m$ mass. (Strings are massless and inextensible)

1. $\frac{15mg}{11}$
2. $\frac{18mg}{13}$
3. $\frac{18mg}{11}$
4. $\frac{15mg}{13}$

Q. A cricket ball of mass 0.2 kg moving with speed 10 m s^–1 collides with a bat and bounce back with same speed within 0.1 s. The force exerted by the bat on ball is

10 m s^–1 चाल से गतिशील 0.2 kg द्रव्यमान वाली क्रिकेट की गेंद एक बल्ले से टकराती है तथा 0.1 s में समान चाल से प्रतिक्षिप्त होती है। बल्ले द्वारा गेंद पर आरोपित बल है

1. 20 N
2. 40 N
3. 60 N
4. Zero
   
   शून्य

Q. Find the acceleration of block $A$ if block $C$ is moving with acceleration $a=3{\text{m/s}}^2$ as shown in the figure. Assume the surface to be frictionless and pulleys and string ideal. Take $g=10m/s^2$

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

Q. Find the displacement travelled by the sphere in $1$ second if the acceleration of the cube is $2{\text{m/s}}^2$. System starts from rest and the sphere remains in contact with the cube.

1. $1\text{m}$
2. $2\text{m}$
3. $\sqrt{2}\text{m}$
4. $\sqrt{3}\text{m}$

Q. In the shown figure two beads slide along a smooth horizontal rod as shown in the figure. The relation between $v$ and $v_0$ in the shown position will be

1. $v=v_o\cot \theta$
2. $v=v_o\sin \theta$
3. $v=v_o\tan \theta$
4. $v=v_o\cos \theta$

Q. In the arrangement shown in the figure, the ends $P$ and $Q$ of an inextensible string move downwards with uniform speed $u$. Pulleys $A$ and $B$ are fixed. What is the speed with which mass $M$ moves up?

1. $2u\cos \theta$
2. $u\cos \theta$
3. $\frac{2u}{\cos \theta }$
4. $\frac{u}{\cos \theta }$

Q. More than One Answer Type
एक से अधिक उत्तर प्रकार के प्रश्न

A block of mass m is placed on smooth horizontal surface at rest. Block is being pulled by constant force F. During the motion

m द्रव्यमान के एक गुटके को किसी चिकने क्षैतिज पृष्ठ पर विराम में रखा जाता है। गुटके को नियत बल F से खींचा जाता है। गति के दौरान

1. Maximum elongation of spring is $\frac{F}{k}$
   
   स्प्रिंग का अधिकतम प्रसार $\frac{F}{k}$ है
2. Maximum elongation of spring is $\frac{2F}{k}$
   
   स्प्रिंग का अधिकतम प्रसार $\frac{2F}{k}$ है
3. Maximum velocity of block is $\frac{F}{\sqrt{mk}}$
   
   गुटके का अधिकतम वेग $\frac{F}{\sqrt{mk}}$ है
4. Maximum velocity of block is $\frac{F}{\sqrt{2mk}}$
   
   गुटके का अधिकतम वेग $\frac{F}{\sqrt{2mk}}$ है

Q. A block of mass $10\text{kg}$ is suspended from a string of length $4\text{m}$. When pulled by a force $F$ along the horizontal from its midpoint, upper half of the string makes an angle ${45}^{\circ }$ with the vertical. The value of $F$ is

1. $100\text{N}$
2. $90\text{N}$
3. $75\text{N}$
4. $70\text{N}$

Q. Find the tension in the string connecting block of mass $M$ and ring of mass $m$ at the instant shown. Assume all surfaces to be frictionless and the ring is constrained to move along the wire only. $M=25\text{kg};m=9\text{kg}$ and $g=10{\text{m/s}}^2$

1. $50\text{N}$
2. $100\text{N}$
3. $125\text{N}$
4. $150\text{N}$

Q. Block $A$ of mass $\frac{m}{2}$ is connected to one end of a light rope which passes over a light frictionless pulley as shown in figure.


A man of mass $2m$ climbs the other end of the rope with a relative acceleration of $\frac{g}{2}$ with respect to rope. Find the acceleration ($a_0$) of block $A$ with respect to ground.

1. $a_0=\frac{g}{2}$
2. $a_0=\frac{2}{3}g$
3. $a_0=\frac{3}{2}g$
4. $a_0=g$

Q. Blocks are at rest & pulled by F & F', find tension force in the string

1. T=13 N
2. T=23 N
3. T=0 N
4. T=18 N

Q. A painter of mass $100\text{kg}$ is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is $450\text{N}$. If the crate weighs $25\text{kg}$ then, find the acceleration of the system and the tension in the rope.

1. $2{\text{ms}}^{-2},750\text{N}$
2. $3{\text{ms}}^{-2},500\text{N}$
3. $4{\text{ms}}^{-2},570\text{N}$
4. $1{\text{ms}}^{-2},50\text{N}$

Q.
Find the acceleration of $B$ if the acceleration of $A$ is $4m/s^2$ . ($B$ is only allowed to move in vertical direction)

1. $\frac{2}{\sqrt{3}}m/s^2$
2. $\frac{4}{\sqrt{3}}m/s^2$
3. $2\sqrt{3}m/s^2$
4. $4\sqrt{3}m/s^2$

Q. A particle is resting on a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. The magnitude of the force increases with time according to law $F=\alpha t$, where $\alpha$ is a constant. For the figure shown which of the following statement is wrong?

1. $\text{Curve 1 shows acceleraion against time}$
2. $\text{Curve 2 shows velocity against time}$
3. $\text{Curve 2 shows velocity against acceleration}$
4. $\text{Curve 1 shows acceleration against velocity}$

Q. Find the velocity of separation of the spheres $1$ and $2$ if the sphere $3$ comes down with a velocity of $3m/s$. Assume all spheres to be identical and frictionless.

1. $2\sqrt{3}m/s$
2. $4\sqrt{3}m/s$
3. $6\sqrt{3}m/s$
4. $8\sqrt{3}m/s$

Q. Find the relation between acceleration of $A\left(a\right)$ and acceleration of $B\left(b\right)$ in the figure shown

1. $a=b\sin \theta$
2. $a=b\cos \theta$
3. $a=b\tan \theta$
4. $a=b\cot \theta$

Q. If masses are released from the position shown in the figure then time elapsed before mass $m_1$ collides with the floor will be

1. $\sqrt{\frac{2m_{1}gd}{m_1+m_2}}$
2. $\sqrt{\frac{2(m_1+m_2)d}{(m_1-m_2)g}}$
3. $\sqrt{\frac{2(m_1-m_2)d}{(m_1+m_2)g}}$
4. None of these

Q. Find the force of interaction between $2kg$ and $1kg$ bodies for the figure shown. (Take $g=10m/s^2$)

1. $25N$
2. $30N$
3. $45N$
4. $50N$

Q. In the figure shown, find the acceleration of the block $B$. Assume all surfaces to be smooth.

1. $a=\frac{3F}{20m}{\text{m/s}}^2$
2. $a=\frac{3F}{21m}{\text{m/s}}^2$
3. $a=\frac{2F}{21m}{\text{m/s}}^2$
4. $a=\frac{3F}{18m}{\text{m/s}}^2$

Q. Same spring is attached with 2kg, 3kg and 1 kg blocks in three different cases as shown in the figure. If $x_1,x_2\text{and}{x}_3$ be the extensions in the spring in these three cases then

1. $x_1=0,x_3>x_2$
2. $x_2>x_1>x_3$
3. $x_3>x_1>x_2$
4. $x_1>x_2>x_3$

Q. In the given figure $V_B$ is (All surfaces are smooth and string is massless and inextensible)

1. $2m/s$
2. $6m/s$
3. $8m/s$
4. $10m/s$

Q. Two pulley arrangements of figure given are identical. The mass of the rope is negligible. In fig (a), the mass $m$ is lifted by attaching a mass $2\text{m}$ to the other end of the rope. In fig (b), $m$ is lifted up by pulling the other end of the rope with a constant downward force $F=2mg$. The acceleration of $m$ in the two cases are respectively

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

Q. The velocity time graph of a lift moving upwards has been shown below. Let $T_1,T_2$ and $T_3$ be the tensions in the elevator cable during the three time intervals $\Delta t_1,\Delta t_2$ and $\Delta t_3$, then $T_1:T_2:T_3$

1. $11:10:9$
2. $19:10:11$
3. $11:10:12$
4. $11:10:8$