Pseudo Force

Q.

A block of mass $1kg$ lies on horizontal surface in a truck. The coefficient of static friction between the block and the surface is ${\mu }_s=0.6$. If the acceleration of the truck is $5m/s^2$, the friction force acting on the block is

1. $4\text{N}$
2. $5\text{N}$
3. $6\text{N}$
4. $7\text{N}$

Q. The ratio of the weight of a man in a stationary lift and when it is accelerating downward with uniform acceleration $a$ is $3:2$. The value of $a$ is (Acceleration due to gravity is $g$ )

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

Q.

The ratio of the weight of a man in a stationary lift and when it is moving downward with uniform acceleration ‘a’ is 3:2. The value of ‘a’ is (g – Acceleration due to gravity on the earth)

1. 

2. 

3. 

4. 

Q.

A person is standing in an elevator. In which situation will he find his weight less than his actual weight?

1. When the elevator moves with an upward constant acceleration

2. When the elevator moves with a downward constant acceleration

3. When the elevator moves upward with uniform velocity

4. When the elevator moves downward with uniform velocity

Q.

Ain't the net acceleration upwards when the lift is going up and deccelerating? or in other case Ain't the net acceleration downwards when the lift is going down and deccelerating? Then why do we feel our weight less and more respectively in the above cases? ( should not it be when the acc is up weight should be felt more than true weight and vice versa)

Q. A small metallic sphere of mass $m$ is suspended from the ceiling of a car accelerating on a horizontal road with constant acceleration $a$ as shown in the figure. The tension in the string attached with the metallic sphere is

1. $mg$
2. $m(g+a)$
3. $m(g-a)$
4. $m\sqrt{g^2+a^2}$

Q. A force $\overrightarrow{F}=(40\hat{i}+10\hat{j})\text{N}$ acts on a body of mass $5\text{kg}$. If the body starts from rest, its position vector $\overrightarrow{r}$ at time $t=10\text{s}$, will be :

1. $(100\hat{i}+400\hat{j})\text{m}$
2. $(100\hat{i}+100\hat{j})\text{m}$
3. $(400\hat{i}+100\hat{j})\text{m}$
4. $(400\hat{i}+400\hat{j})\text{m}$

Q. A person of mass 50 kg stands on a weighing scale on a lift. If the lift is ascending upwards with a uniform acceleration of $9m{s}^{-2}$, what would be the reading of the weighing scale? (Take $g=10m{s}^{-2}$)

1. 50 kg
2. 60 kg
3. 95 kg
4. 100 kg

Q.

A monkey of mass 40 kg climbs on a rope (Fig. 5.20) which can stand a maximum tension of 600 N. In which of the following cases will the rope break: the monkey

(a) climbs up with an acceleration of 6 m s^–2

(b) climbs down with an acceleration of 4 m s^–2

(c) climbs up with a uniform speed of 5 m s^–1

(d) falls down the rope nearly freely under gravity?

(Ignore the mass of the rope).

Fig. 5.20

Q. A hydraulic press can lift $100\text{kg}$ when a mass $m$ is placed on the smaller piston. It can lift _______ $\text{kg}$ when the diameter of the larger piston is increased by $4$ times and that of the smaller piston is decreased by $4$ times keeping the same mass $m$ on the smaller piston.

Q. The rear side of a truck is open and a box of $40\text{kg}$ mass is placed $5\text{m}$ away from the open end as shown. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road, the truck starts from rest and accelerates with $2{\text{ms}}^{-2}$. At what distance from the starting point does the box fall off the truck (i.e., distance travelled by the truck)? [Ignore the size of the box]

1. $40\text{m}$
2. $50\text{m}$
3. $30\text{m}$
4. $20\text{m}$

Q. A block is placed on an inclined plane moving towards right horizontally with an acceleration $a_0=g$. The length of the plane $AC$ = $1\text{m}$. Friction is absent everywhere. The time taken by the block to reach from $C$ to $A$ is approximately $(g=10{\text{m/s}}^2)$

1. $1.2$ $s$
2. $0.74s$
3. $2.56s$
4. $0.42s$

Q.

A body of mass $1kg$ rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force $FN$. The value of F will be __________. (Round off to the Nearest Integer) [$g=10m{s}^{-2}$]

Q. If a stone is thrown out of an accelerated train, then acceleration of the stone at any instant depends on

1. force acting on it at that instant.
2. acceleration of the train.
3. Both (a) and (b)
4. None of these

Q. A bead of mass $m$ is attached to one end of a spring of natural length 𝑅 and spring constant $K=\left(\right(\sqrt{3}+1\left)\text{mg}\right)/R$ . The other end of spring is fixed at a point $A$ on a smooth vertical ring of radius $R$ as shown in the figure. The normal reaction at $B$ just after it is released to move is

1. $mg/2$
2. $3\sqrt{3}mg$
3. $\sqrt{3}mg$
4. $3\sqrt{3}mg/2$

Q.

If ${10}^{22}$ gas molecules each of mass ${10}^{-26}kg$ collide with a surface (perpendicular to it) elastically per second over an area $1m^2$ with a speed ${10}^{4}m/s$, the pressure exerted by the gas molecules will be of the order of

1. ${10}^{8}N/m^2$

2. ${10}^{3}N/m^2$
3. ${10}^{4}N/m^2$
4. $2N/m^2$

Q. A block is kept on a frictionless inclined surface with angle of inlcination $\alpha$. The inclined wedge is given an acceleration $a$ to keep the block stationary with respect to the inclined plane. Then magnitude of acceleration $a$ is equal to

1. $\frac{g}{\tan \alpha }$
2. $g\text{cosec}\alpha$
3. $g\tan \alpha$
4. $g$

Q. Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity $\frac{v_A}{v_B}$ is

Q.

A person of mass $50kg$ stands on a weighing scale on a lift if the lift is descending with a downward acceleration of $9\frac{m}{s^2}$. what would be the reading of the weighing scale

Q. With what acceleration 'a' should the box in figure descend so that the block of mass M exerts a force $\frac{Mg}{4}$ on the floor of the box?

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

Q. A car is moving on a plane inclined at ${30}^{\circ }$ to the horizontal with an acceleration of $9.8m/s^2$ parallel to the plane upward. A bob is suspended by a string from the roof. The angle in degrees which the string makes with the vertical is: (Assume that the bob does not move relative to car and $g=9.8m/s^2$)

1. ${20}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. With what minimum acceleration can a fireman slide down a rope whose breaking strength is $\frac{2}{3}$ of his weight?
(Hint:-Use the concept of pseudo-force.)

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

Q. In the figure the reading of the spring balance will be $:[g=10\frac{m}{s^2}]$

1. $50N$
2. $40N$
3. $60N$
4. $70N$

Q. A downward force of $100\text{N}$ is applied to the small piston with a diameter of $50\text{cm}$ in the hydraulic lift system as shown in figure. What will be the upward force exerted on the large position with a diameter of $1\text{m}$?

1. $300\text{N}$
2. $50\text{N}$
3. $400\text{N}$
4. $600\text{N}$

Q. Two mass $\text{A}$ and $\text{B}$, each of mass $m$, are initially in equilibrium as shown in figure. The acceleration of block $A$ just after string between $\text{A}$ and $B$ is cut will be :
( $g=$ acceleration due to gravity).

1. $2g$ downward
2. $2g$ upward
3. $g$ downward
4. $g$ upward

Q. A person of mass $60\text{kg}$ is in a lift. The change in the apparent weight of the person, when the lift accelerates up with an acceleration of $2{\text{m/s}}^2$ and then down with an acceleration of $2{\text{m/s}}^2$ is

1. $120\text{N}$
2. $240\text{N}$
3. $480\text{N}$
4. $720\text{N}$

Q. A bob of mass ${}^{\prime }{m}^{\prime }$ is attached to ceiling of a lift with the help of string as shown. Calculate tension in string when lift is accelerated up with acceleration ${}^{\prime }{a}^{\prime }$.

1. $m(g+a)$
2. $m\sqrt{g^2+a^2}$
3. $mg$
4. $m(g-a)$

Q.

A body slipping on a rough horizontal plane moves with a deceleration of 4.0 $m/s^2$ With a deceleration of kinetic friction between the block and the plan?

Q. A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hands of a person standing in the car. The car is moving with constant acceleration $a$ directed horizontally as shown. The other end of the string is pulled with constant acceleration $a$ vertically down. Find the tension in the string.

1. $m\sqrt{g^2+a^2}$
2. $m(g+a)$
3. $m\sqrt{g^2+a^2}+ma$
4. $m\sqrt{g^2+a^2}-ma$

Q.

A cylindrical vessel of diameter 12 cm contains $800\pi c{m}^3$ of water. A cylindrical glass piece of diameter 8.0 cm and height 8.0 cm is placed in the vessel. If the bottom of the vessel under the glass piece is seen by the paraxial rays (see figure), locate its image. The index of refraction of glass is 1.50 and that of water is 1.33.