Problems with Pseudo Force

Q. A block of mass m is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally, so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be:

1. $mg\sin \theta$
2. $\text{mg}$
3. $mg\cos \theta$
4. $\frac{mg}{\cos \theta }$

Q.

The maximum distance up to which TV transmission from a TV tower of height h can be received is proportional to

Q. If the coefficient of friction between $A$ and $B$ is $\mu$, the maximum acceleration of the wedge $A$ for which $B$ will remain at rest with respect to the wedge is:

1. $\mu g$
2. $g\left(\frac{1+\mu }{1-\mu }\right)$
3. $g\left(\frac{1-\mu }{1+\mu }\right)$
4. $\frac{g}{\mu }$

Q. In the arrangement shown in figure pulley and strings are ideal. End $A$ of string connected to pulley $P_1$ is moved upwards with acceleration $a_A=2m/s^2$ while end $B$ of another string shown in figure is moved up with acceleration $a_B=1m/s^2$. Block $C$ of mass $1kg$ is moving up with acceleration $1m{s}^2$. If block $D$ to which string are connected symmetrically moves such that its orientations remains same, then choose the correct statements. (assume $g=10m/s^2)$

1. Acceleration of block $D$ is $\frac{1}{2}$ $m/s^2$ upwards
2. End $A$ is pulled with force of $22N$
3. Mass of block $B$ is $\frac{1}{2}kg$
4. acceleration of block $B$ is $\frac{7}{3}m{s}^{-2}$ upwards

Q. A square plate ABCD of side length a and mass m is suspended by two identical strings in vertical plane as shown in figure. As soon as right string connecting vertex B is cut,

1. tension of left string becomes $\frac{2mg}{5}$.
2. angular acceleration of plate is $\frac{3g}{4a}$.
3. acceleration of center of plate is $\frac{3g}{5}$.
4. acceleration of vertex A is zero.

Q. A block is placed on the top of a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation $a$, the block is released. The acceleration of the block relative to the incline is

1. $\text{g sin}\theta$
2. $\text{a sin}\theta$
3. $(g-a)\text{sin}\theta$
4. $(g+a)\text{sin}\theta$

Q. A pulley system is attached to an elevator as shown in figure. The elevator starts to move up with an acceleration $a$.

Match statements in column I with results in column II.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(a)}& \text{Acceleration of}{m}_1\text{in elevator frame}& \text{(p)}& \frac{1}{2}\left(\frac{(m_2-m_1)g+2m_{2}a}{m_1+m_2}\right)t^2\\ \text{(b)}& \text{Acceleration of}{m}_1\text{in ground frame}& \text{(q)}& \frac{1}{2}\left[\frac{m_2-m_1}{(m_1+m_2)}\right(g+a\left)\right]t^2\\ \text{(c)}& \text{Distance covered of}{m}_1\text{in elevator frame}& \text{(r)}& \left(\frac{m_2-m_1}{m_1+m_2}\right)g+\left(\frac{2m_2}{m_1+m_2}\right)a\\ \text{(d)}& \text{Distance covered of}{m}_1\text{in ground frame}& \text{(s)}& \frac{(m_2-m_1)}{(m_1+m_2)}(g+a)\\ & & \text{(t)}& \text{None of the above}\end{array}$

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

Q.

The friction coefficient between the board and the floor shown in figure (6-E7) is $\mu .$ Find the maximum force that the man can exert on the rope so that the board does not slip on the floor.

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

Q.

A man has fallen into a ditch of width d and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in figure. Show that the force (assumed equal for both the friends) exerted by each friend on the road increases as the man moves up . Find the force when the man is at a depth h.

Q. Two bodies of mass 2 kg and 3 kg are connected to the ends of a string of negligible mass passing over a frictionless pulley . Calculate the acceleration of two bodies and tension in the string.

Q. The rear side of a truck is open and a box of mass $20\text{kg}$ is placed on the truck $4\text{m}$ away from the open end. The coefficient of friction between the box and the surface is $0.15$. The truck starts from rest with an acceleration of $2{\text{m s}}^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to (take $g=10m{s}^{-2}$)

1. $4\text{m}$
2. $32\text{m}$
3. $8\text{m}$
4. $16\text{m}$

Q. In the arrangement shown in the figure mass of the block $B$ and $A$ are $2m,8m$ respectively. Surface between $B$ and floor is smooth. The block $B$ is connected to block $C$ by means of a pulley. If the whole system is released then the minimum value of mass of the block $C$ so that the block $A$ remains stationary with respect to $B$ is (Co-efficient of friction between $A$ and $B$ is $\mu$)

1. $\frac{m}{\mu }$
2. $\frac{10m}{\mu -1}$
3. $\frac{2m}{\mu +1}$
4. $\frac{10m}{1-\mu }$

Q.

A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling. If it wishes to go up with an acceleration of 1$m/s^2$, how much force should it apply to the rope ? If the rope is 5m long and the monkey starts from rest, how much time will it take to reach the ceiling ?

Q.

A brick of mass 2 kg begins to slide down on a plane inclined at an angle of ${45}^o$ with the horizontal. The force of friction will be

1. 19.6 sin 45^o

2. 9.8 sin 45^o

3. 19.6 cos 45^o

4. 9.8 cos 45^o

Q. Find the force exerted by $5\text{kg}$ block on floor of lift, as shown in figure. (Take $g=10m/s^2)$

1. 100 N
2. 115 N
3. 105 N
4. 135 N

Q. Two bodies of mass $1\text{kg}$ and $2\text{kg}$ are tied to an ideal string. The string passes over a smooth pulley as shown in the figure. The acceleration of the $2\text{kg}$ block is

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

Q. A block of mass 'm' is hanging to a string in an elevator. The elevator is moving up with an acceleration 'a'. What will be the tension in the string?

1. ma
2. m(g-a)
3. mg
4. m(g+a)

Q. A light and smooth pulley is attached to the ceiling of a lift moving upward with acceleration $a_0=2{\text{m/s}}^2$ as shown in the figure. Two blocks of equal masses $(m=3\text{kg})$ are attached to the two ends of a massless string passing over the pulley. Find the tension in the string. (Take $g=10{\text{m/s}}^2$).

1. $12\text{N}$
2. $24\text{N}$
3. $10\text{N}$
4. $36\text{N}$

Q. A block of mass $M$ is placed on a rough floor of a lift. The coefficient of friction between the block and the floor is $\mu$. When the lift falls freely, the block is pulled horizontally on the floor. What will be the force of friction?

1. $\mu Mg$
2. $\frac{\mu Mg}{2}$
3. $2\mu Mg$
4. None of these

Q. Two blocks of mass $m=5kg$ and $M=10kg$ are connected by a string passing over a pulley $B$ as shown. Another string connects the centre of pulley $B$ to the floor and passes over another pulley $A$ as shown. An upward force $F$ is applied at the centre of pulley $A$. Both the pulleys are mass-less. An upward force $F$ is applied in the pulley $A$. Find the acceleration of blocks $m$ and $M$, if $F$ is $100N$.

1. $10m/s^2;5m/s^2$
2. $5m/s^2;2.5m/s^2$
3. $2.5m/s^2;5m/s^2$
4. $0m/s^2;0m/s^2$

Q.

Two blocks of mass 10g and 30g are fastened over a frictionless pulley . The 10g block rests on the table what minimum force must be applied on the 10g block to keep it on table ? What will be the tension in the cord ? What will be the acceleration of the system and the tension in the cord when force is withdrawn?

Q.

A car starts from rest on a half kilometer long bridge. The coefficient of friction between the tyre and the road is 1.0. Shwo that one cannot drive through the bridge in less tahn 10 s.

Q. A circular disc of mass m and radius R is placed on horizontal surface of coefficient of friction $\mu$. The disc is given an angular velocity $\omega$. Plane of disc is horizontal and there is no initial velocity of the center of mass.

1. Net torque acting on disc is $\frac{\mu mgR}{3}$

2. Net friction force acting on disc is $\mu mg$

3. Time after which disc stops rotating is $\frac{3wR}{4\mu g}$
4. Center of mass of disc will not displace

Q. What will be the reading of spring balance shown in the figure, if it is moving in upward direction with a constant acceleration $a=2{\text{m/s}}^2$ and an initial velocity $v=2\text{m/s}$. (Take $g=10{\text{m/s}}^2$)

1. $80\text{N}$
2. $100\text{N}$
3. $120\text{N}$
4. $140\text{N}$

Q.

A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

1. Rise from the middle

2. Lowered equally

3. Rise equally

4. Rise from the sides

Q.

A massive platform of mass M is moving horizontally with speed v = 6 ms${}^{-1}$. At t = 0 a body of mass m (m << M) is gently placed on the platform. If coefficient of friction between body and platform is $\mu$ = 0.3 and g = 10 m/s${}^2$, then

1. The body covers a distance 3 m on the platform in the direction of motion of the platform.

2. The body covers a distance 3 m on the platform opposite to the direction of motion of platform before coming to rest.

3. The body covers a distance of 6 m on the platform opposite to the direction of motion of platform before coming to rest.

4. The body covers a distance of 6 m on the platform in the direction of motion of the platform.

Q. Co-efficient of friction between $5\text{kg}$ and $10\text{kg}$ blocks is $0.5$. If friction between them is $20\text{N}$. What is the value of force being applied on $5\text{kg}$. Assume the floor is friction less.

1. $10\text{N}$
2. $20\text{N}$
3. $30\text{N}$
4. $40\text{N}$

Q. Find the force exerted by 5 kg block on floor of lift, as shown in figure. $(Takeg=10m/s^2)$

1. 100 N
2. 115 N
3. 105 N
4. 135 N

Q. A particle is projected with a velocity $u$ at two different angles which are complementary to each other. If $H_1$ and $H_2$ are the heights attained by them in each case, find the range of the particle.

1. $4\sqrt{H_1{H}_2}$
2. $2\sqrt{H_1{H}_2}$
3. $\sqrt{H_1{H}_2}$
4. $\frac{1}{2}\sqrt{H_1{H}_2}$