Problem Solving

Q. A rope of length $10m$ and linear mass density $4kg/m$ is lying lengthwise on a horizontal smooth table. One end of the rope is pulled horizontally by a force of $40N$. The tension in the rope at a point $4m$ from point of application of force will be

1. $40N$
2. $24N$
3. $15N$
4. $49N$

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.

The time period of a simple pendulum in a satellite is:

Q.

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the force? Also, name the triangle formed by the forces as sides

1. $60°$ equilateral triangle

2. $120°$ equilateral triangle

3. $120°,30°,30°$ an isosceles triangle

4. $120°$ an obtuse-angled triangle

Q.

What is the angle of banking? Derive the expression for the angle of banking on a curved road with a certain coefficient of friction.

Q.

Explain the difference between static friction and kinetic friction. Which is greater?

Q. The force F is given by expression F=A cos(Bx)+C sin(Dt), where x is the displacement and T is the time. Then dimension of D/B are same as the of

Q. When two charged particles are placed at the certain distance apart in vacuum, then the force experienced by one of the charges is equal to $F.$ If vacuum is replaced by a medium of dielectric constant $6,$ then the net force experienced by the charged particle will be equal to

$[$0.77 Mark$]$

1. $6F$
2. $F$
3. $\frac{F}{6}$
4. $\frac{F}{12}$

Q. The blocks are of mass $2\text{kg}$ shown, is in equilibrium. At $t=0$ right spring in figure (i) and right string in figuree (ii) breaks. Find the ratio of instantaneous acceleration of blocks in fig (i) and fig (ii) (Take $g=10m/s^2$)

1. $\frac{24}{25}$
2. $\frac{25}{24}$
3. $\frac{24}{27}$
4. $\frac{30}{27}$

Q.

What is a free body diagram?

Q. Arrangement of two block system is as shown. The net force acting on $1\text{kg}$ and $2\text{kg}$ blocks are (assuming the surfaces to be frictionless) respectively.

1. $4\text{N},8\text{N}$
2. $1\text{N},2\text{N}$
3. $2\text{N},4\text{N}$
4. $3\text{N},6\text{N}$

Q. A body of mass $2\text{kg}$ is hung on a spring balance mounted vertically in a lift. If the lift moves up with an acceleration equal to the acceleration due to gravity, the reading on the spring balance will be

1. $2\times g\text{kg}$
2. $4\times g\text{kg}$
3. $2\text{kg}$
4. $4\text{kg}$

Q. A sphere of radius $R$ is in contact with a wedge. The point of contact is $\frac{R}{5}$ from the ground as shown in the figure. Wedge is moving with velocity $20m{s}^{-1}$ towards left. The velocity of the sphere at this instant will be

1. $12m{s}^{-1}$
2. $16m{s}^{-1}$
3. $20m{s}^{-1}$
4. $15m{s}^{-1}$

Q. In the figure, accelerations of blocks $A$, $B$ and $C$ are indicated by $a$, $b$, and $c$ respectively. Acceleration $b$ and $c$ are w.r.t to the ground. Find the acceleration of the body $A$ in terms of $b$ and $c$ with respect to the ground if the surface is smooth and pulley and string is ideal.

1. $\sqrt{(b+c{)}^2+a^2}$
2. $c-(a+b)\cos \theta$
3. $\sqrt{(b+c{)}^2+c^2-2(b+c).c.\cos \theta }$
4. $\sqrt{(b+c{)}^2+c^2+2(b+c).c.\cos \theta }$

Q. What is the reading of the spring balance in the following device?

1. $\frac{20}{3}\text{kg}$
2. $\frac{40}{3}\text{kg}$
3. $\frac{10}{3}\text{kg}$
4. $\frac{1.5}{3}\text{kg}$

Q. Two forces $\overrightarrow{F_1}=500N$due east and $\overrightarrow{F_2}=250N$ due north have their common initial point. $\overrightarrow{F_2}-\overrightarrow{F_1}$ is

1. $250\sqrt{5}N,{\tan }^{-1}\left(2\right)$west of north
2. $750N,{\tan }^{-1}\left(\frac{3}{4}\right)$ North of West
3. $250N,{\tan }^{-1}\left(2\right)$west of north
4. $0$

Q. How viscosity is different from the friction?

Q. The ratio of surface tensions of mercury and water is given to be $7.5$ while the ratio of their densities is $13.6$. Their contact angles, with glass, are close to $135°$ and $0°$, respectively. It is observed that mercury gets depressed by an amount $h$ in a capillary tube of radius $r_1$, while water rises by the same amount $h$ in a capillary tube of radius $r_2$. The ratio, $\left(\frac{r_1}{r_2}\right)$, is then close to

1. $3/5$
2. $2/3$
3. $2/5$
4. $4/5$

Q. A bob weighing 50 grams hangs vertically at the end of string 50 cm long. If 20 gram force is applied horizontally, by how much distance the Bob is pulled aside from its initial position when it reaches in equilibrium position?

Q. A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity $v=(5t\hat{i}+2t\hat{j})m/s$. Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take $g=10m/s^2$)

1. 
2. 
3. 
4. 

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. $11:10:8$

Q. An unbanked curve has a radius of 60 m. The maximum speed at which a car can make a turn if the coefficient of static friction is 0.75, is

1. 2.1 m/s
2. 7 m/s
3. 21 m/s
4. 14 m/s

Q.

A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is

1. Halved

2. Unchanged

3. Quadrupled

4. Doubled

Q. An inclined plane makes an angle ${30}^{\circ }$ with the horizontal. A groove $OA=5\text{m}$ cut in the plane makes an angle ${30}^{\circ }$ with $OX$. A short smooth cylinder is free to slide down the influence of gravity. Find the time taken by the cylinder to reach from $A$ to $O$.
$(\text{Take}g=10{\text{m/s}}^2)$

1. $3\text{s}$
2. $1\text{s}$
3. $2\text{s}$
4. $4\text{s}$

Q. When a long glass capillary tube of radius $0.015\text{cm}$ is dipped in a liquid, the liquid rises to a height of $15\text{cm}$ within it. If the contact angle between the liquid and glass to close to $0^{\circ },$ the surface tension of the liquid (in ${\text{mN m}}^{-1}$) is ______.
(Give answer in the closest integer)

[${\rho }_{\text{(liquid)}}=900{\text{kg m}}^{-3},g=10{\text{ms}}^{-2}$]

Q.

Why it is easy to push lawn roller as compared to pull it?

Q. If the thrust on a rocket moving with a velocity of $300\text{m/s}$ is $210\text{N}$, the rate of combustion of the fuel is

1. $0.007\text{kg/s}$
2. $1.4\text{kg/s}$
3. $0.7\text{kg/s}$
4. $10.7\text{kg/s}$

Q. A particle is projected from point ${}^{\prime }{A}^{\prime }$ , that is at a distance $4R$ from the centre of the Earth, with speed $V_0$ as shown. If the particle passes grazing the earth's surface, then it is found that $V_0=4000\times \sqrt{N}$. Find the value of N.
[Take $\frac{GM}{R}=6.4\times {10}^7\frac{{\text{m}}^2}{{\text{s}}^2}$]

Q.

Why torque is maximum at 90 degrees ?

Q. The maximum value of static friction that develops on a body when the body just tends to slide over the surface of another body is
A kinetic friction
B rolling friction
C limiting friction
D none of these