Normal Force

Q. A block of mass $m$ is placed on the floor of lift which is moving with velocity $v=4t^2$, where $t$ is time in second and velocity in $\text{m/s}$. Find the time at which normal force on the block is three times of its weight.

1. $\left(\frac{3g}{8}\right)s$
2. $\frac{g}{4}s$
3. $3gs$
4. $gs$

Q. What is the actual weight of a molecule of water?

Q. Two points sources separated by $2.0\text{m}$ are radiating in phase with $\lambda =0.50\text{m}.$ A detector moves in a circular path around the two sources in a plane containing them. How many maxima are detected ?

1. $16$
2. $20$
3. $24$
4. $32$

Q. The elevator shown in the figure is descending with an acceleration of $2{\text{ms}}^{-2}$. The mass of the block $A=0.5\text{kg}$. The force exerted by the block $A$ on the block $B$ is $(g=10{\text{ms}}^{-2})$

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

Q. Two identical blocks $\text{A}$ and $\text{B}$ of mass $1\text{kg}$ are joined together with a massless spring and are placed on a smooth surface as shown in the figure. If the block $\text{A}$ moves with an acceleration of $3{\text{m/s}}^2$, then the acceleration of the block $\text{B}$ is:

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

Q. In case of circular motion of a body, if tangential force also acts on the body in addition to centripetal force, then work done:

1. by both the forces is positive
   
2. by tangential force is zero by work done by centripetal force is not zero.
   
3. by both the forces is zero
   
4. by centripetal force is zero but work done by tangential force is not zero
   

Q. An automobile of mass ${}^{\prime }{m}^{\prime }$ accelerates starting from origin and initailly at rest, while the engine supplies constant power $P$ . The position is given as a function of time by :

1. $\left[\sqrt{\left(\frac{9p}{8m}\right)}\right]t^{\frac{3}{2}}$
2. $\left[\sqrt{\left(\frac{8p}{9m}\right)}\right]t^{\frac{2}{3}}$
3. $\left[\sqrt{\left(\frac{9m}{8p}\right)}\right]t^{\frac{3}{2}}$
4. $\left[\sqrt{\left(\frac{8p}{9m}\right)}\right]t^{\frac{3}{2}}$

Q.

A particle is projected with a speed u at an angle $\theta$ with the horizontal. Consider a small part of its path near the highest position and take it approximately to be a circular arc. What is the radius of this circle ? This radius is called the radius of curvature of the curve at the point.

Q. Two blocks of mass $M_1=20\text{kg}$ and $M_2=12\text{kg}$ are connected by a metal rod of mass $8\text{kg}$. The system is pulled vertically up by applying a force of $480\text{N}$ as shown. The tension at the mid-point of the rod is:

1. $\text{144 N}$
2. $\text{96 N}$
3. $\text{240 N}$
4. $\text{192 N}$

Q.

What factors effect acceleration?

Q. A $900kg$ elevator hangs by a steel cable for which the allowable stress is $1.15\times {10}^{8}N/m^2$. What is the minimum diameter required if the elevator accelerates upward at $1.5m/s^2$. Take $g=10m/s^2$

1. 
   $\frac{6\times {10}^{-2}}{\sqrt{10\pi }}M$
   
2. 
   $\frac{6\times {10}^{-2}}{\sqrt{5\pi }}M$
   
3. 
   $\frac{3\times {10}^{-2}}{\sqrt{5\pi }}M$
   
4. 
   $\frac{6\times {10}^{-2}}{\sqrt{10\pi }}M$
   

Q.

Is gravity the strongest force in the universe?

Q. Statement – 1: Normal reaction acting on a body is always perpendicular to the surface. Statement – 2: Normal reaction is a component of contact force.

1. STATEMENT – 1 is True, STATEMENT – 2 is True; STATEMENT – 2 is a correct explanation for STATEMENT – 1
2. STATEMENT – 1 is True, STATEMENT – 2 is True; STATEMENT – 2 is NOT a correct explanation for STATEMENT – 1
3. STATEMENT – 1 is True, STATEMENT – 2 is False
4. STATEMENT – 1 is False, STATEMENT-2 is True

Q. The moment of inertia of a circular disc of mass $M$ and radius $R$ about an axis passing through the center of mass is $I_0$. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is,

1. $2I_0$
2. $8I_0$
3. $\frac{I_0}{4}$
4. $\frac{I_0}{8}$

Q. At surface of earth weight of a person is $72N$ then his weight at height $R/2$ from surface of earth is $(R=\text{radius of earth})$

1. $72N$
2. $16N$
3. $28N$
4. $32N$

Q. Four blocks are arranged on a smooth horizontal surface as shown in the figure. The maximum value of horizontal force $F$, applied to one of the bottom blocks that makes all four blocks move with the same acceleration, is -

1. $\mu mg[\frac{m+M}{2m+M}]$
2. $2\mu mg[\frac{m+M}{2m+M}]$
3. $3\mu mg[\frac{m+M}{2m+M}]$
4. $0.5\mu mg[\frac{m+M}{2m+M}]$

Q.

The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite to the direction of velocity and is proportional to it. The balloon carries a mass M ans id found to fall down near the earth's surface with a constatnt velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v ?

Q. What should be the acceleration ${}^{\prime }{a}^{\prime }$ of the box shown in figure so that the block of mass $m$ exerts a force $\frac{mg}{4}$ on the floor of the box ? (where $g$ is acceleration due to gravity)

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

Q. A body of radius $R$ and mass $m$ is rolling smoothly with speed $v$ on a horizontal surface. It then rolls up a hill to a maximum height h. If $h=\frac{3v^2}{4g}$, what might the body be?

1. a solid circular cylinder
2. a hollow circular sphere
3. a solid circular sphere
4. a hollow circular cylinder

Q. Is it possible to open the cap of a pen with one finger. Why?

Q. A disc of mass ${}^{\prime }{m}^{\prime }$ and radius $R$ is placed on a smooth horizontal floor such that the plane surface of the disc is in contact with the floor. A man of mass $m/2$ stands on the disc at its periphery. The man starts walking along the periphery of the disc. The size of the man is negligible as compared to the size of the disc. Then the centre of disc.

1. moves along a circle of radius $R$
2. does not move along a circle
3. moves along a circle of radius $R/3$
4. moves along a circle of radius $R/2$

Q. Which factor provide a centripetal force in the following cases:
i) revolution of electron around the nucleus.
ii) revolution of earth around the sun.
iii) circular motion of a cyclist.

Q. You lift a heavy book from the floor of the room and keep it in the bookshelf having a height $2m$. In this process you take $5\text{seconds}$. The work done by you will depend upon

1. Mass of the book and time taken
2. Weight of the book and height of the bookshelf
3. Mass of the book, height of the bookshelf and time taken
4. Height of the bookshelf and time taken

Q.

Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to block of mass M as shown in the figure. The magnitude of force P is:

1. mg cos

2. (M + m) g cosec

3. g tan

4. (M + m)g tan

Q. Three blocks $m_1,m_2$ and $m_3$ of masses $8\text{kg},3\text{kg}$ and $1\text{kg}$ are placed in contact on a smooth surface. Forces $F_1=140\text{N}$ and $F_2=20\text{N}$ are acting on blocks $m_1$ and $m_3$ respectively as shown. The reaction between blocks $m_2$ and $m_3$ is

1. $2.5\text{N}$
2. $7.5\text{N}$
3. $2.5\text{N}$
4. $30\text{N}$

Q. Figure shows a cubical box that has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length 40 cm. The z coordinate of the centre of mass of the box in cm, is

Q.

Two blocks are kept in contact as shown in the figure.

Find the value of normal force exerted by the vertical wall on $20kg$ block. (Assume all surfaces are smooth)

$(\text{Take}g=10{\text{m/s}}^2)$

1. $25N$
2. $75N$
3. $100N$
4. $200N$

Q.

A cold soft drink is kept on the balance. When the cap is open, then the weight

1. Decreases

2. First increases then decreases

3. Increases

4. Remains same

Q. Two masses $A$ and $B$ of $5\text{kg}$ and $6\text{kg}$ are connected by a string passing over a frictionless pulley fixed at the corner of table as shown in figure. The coefficient of friction between $A$ and the table is $0.3$. The minimum mass of $C$ that must be placed on $A$ to prevent it from moving is equal to: $(\text{Take}=10{\text{m/s}}^2)$

1. $10\text{kg}$
2. $15\text{kg}$
3. $5\text{kg}$
4. $3\text{kg}$

Q. You are shown a photo of a car driven on a vertical inside wall of a huge cylinder of radius $50m$. The coefficient of static friction between the car tires and the cylinder is ${\mu }_s=0.8$. The minimum speed $\text{(in m/s)}$ at which the car can be driven like that is $5x$. Find $x$.