Torque Due to Gravity

Q.
Shown in the figure is a rigid and uniform one meter long rod $AB$ held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass $m$ and has another weight of mass $2m$ hung at a distance of $75\text{cm}$ from $A$. The tension in the string at $A$ is :

1. $0.5mg$
2. $2mg$
3. $0.75mg$
4. $1mg$

Q. A block of base 10 cm $\times$ 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is 3. The inclination $\theta$ of this inclined plane from the horizontal plane is gradually increased from $0^o.$ Then

1. at $\theta ={30}^o$, the block will start sliding down the plane
2. the block will remain at rest on the plane up to certain $\theta$ and then it will topple
3. at $\theta ={60}^o$ the block will start sliding down the plane and continue to do so at higher angles
4. at $\theta ={60}^o,$ the block will start sliding down the plane and on further increasing $\theta ,$ it will topple at certain $\theta$

Q. ntAprojectile is thrown at an angle (theta) and (90-theta) from the same point with same velocity 98 m/s .The heights attained by them if the difference of heights is 50 m will be (m)n

Q. Under equilibrium condition which is true? delta s=Zero Delta h=0 Delta h >0 Delta h <0 Delta s>0

Q.

A uniform solid cylinder of mass 'm' can rotate freely about its axis which is kept horizontal. A particle of mass $m_0$ hangs from the end of a light string wound round the cylinder. When the system is allowed to move, the acceleration with which the particle descends is

1. $\frac{2m_{0}g}{m_0+2m}$
2. $\frac{2m_{0}g}{m+2m_0}$
3. $\frac{m_{0}g}{m+m_0}$
4. $\frac{2m_{0}g}{m+2m_0}$

Q. In a physical balance working on the principle of moments, when $5\text{mg}$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

1. Left arm is longer than the right arm
2. Left arm is shorter than the right arm
3. Every object that is weighed using this balance appears lighter than its actual weight.
4. Both the arms are of same length

Q. ntA uniform meter stick of mass m is pivoted about a horizontal axis through its lower end O. It is held vertical and is allowed to fall freely. Ita angular velocity at the instant when it makes angle 60 degree with the verticaln nta. root g/3n ntb. root 3g/2n ntc. root g/4n ntd. root 2g/3n

Q. A square plate of side '4M' has uniform mass density and hinged at the midpoint of one of its edge as shown in figure. What will be the torque due to gravity on it about the hinged point A? $(M=20kg;g=\frac{10m}{s^2})$

1. 300 N-m
2. 200 N-m
3. 100 N-m
4. 400 N-m

Q.

A uniform solid cylinder of mass 'm' can rotate freely about its axis which is kept horizontal. A particle of mass $m_0$ hangs from the end of a light string wound round the cylinder. When the system is allowed to move, the acceleration with which the particle descends is

1. $\frac{2m_{0}g}{m_0+2m}$
2. $\frac{2m_{0}g}{m+2m_0}$
3. $\frac{m_{0}g}{m+m_0}$
4. $\frac{2m_{0}g}{m+2m_0}$

Q. A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its end with a uniform angular velocity $\omega$. The force exerted by the liquid at other end is __________?

1. $\left(M{\omega }^{2}L\right)/2$
2. $M{\omega }^{2}L$
3. $\left(M{\omega }^{2}L\right)/4$
4. $\left(M{\omega }^2{L}^3\right)/2$

Q. A ruler scale is balanced with two fingers, $F_{1}and{F}_2$ at a separation 20 cm and 40 cm from O respectively. If the person balancing the ruler tries to bring his fingers closer to the centre, which finger will slide first?

1. $F_2$
2. Insufficient data
3. $F_1$
4. Both simultaneously

Q. A huge rod whose length is comparable to the radius of the Earth is suspended from the sky. The centre of gravity will be at its centre of mass. This statement is?

1. true
2. false

Q.

what does it mean? - the entire mass of any object is at the center of the earth

Q. Assertion :Polishing of a surface decreases the coefficient of friction up to a certain limit; beyond which it increases. Reason: The friction force arises in parts, as one peak blocks the motion of another peak from the opposite surface and in part from chemical bonding of two opposing peaks as they come in contact.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Is it possible to open a pen cap with one finer? why ?

Q. A massless string is wrapped around a disc of mass $M$ and radius $R$. Another end is tied

1. $\sqrt{2gh}$
2. $\sqrt{2gh\frac{M}{m}}$
3. $\sqrt{2gh\frac{m}{M}}$
4. $\sqrt{\frac{4mgh}{2m+M}}$

Q. Find the maximum value of $M/m$ in the situation shown in figure (6-W10) so that the system remains at rest. Friction coefficient at both the contacts is $\mu$. Discuss the situation when $\tan \theta <\mu$.

Q. Two particles of equals mass 'm' go around a circle of radius R under the action of their mutual gravitational attraction . The speed of each prticle with respect to their centre of mass is :-

1. $\sqrt{\frac{Gm}{R}}$
2. $\sqrt{\frac{Gm}{4R}}$
3. $\sqrt{\frac{Gm}{3R}}$
4. $\sqrt{\frac{Gm}{2R}}$

Q. Three identical rods are joined and hinged at A as shown. If the angle made by the rod AB with vertical in equilibrium is $\theta$, then $\theta$ is

1. $30°$
2. $60°$
3. $37°$
4. $53°$

Q. A ball is placed in a trough as shown. This can be categorised as?

1. Unstable Equilibrium
2. Stable Equilibrium
3. Neutral Equilibrium

Q. A metal cube of side $1m$ is subjected to a uniform force acting normally on the whole surface of the cube, If the volume changes by $1.5\times {10}^{-5}{m}^2$ and if the pressure is ${10}^6$ Pa, find the bulk modulus of the metal.

1. $6.67\times {10}^{10}{N/m}^3$
2. $3.90\times {10}^5{N/m}^3$
3. $5.24\times {10}^5{N/m}^3$
4. $7.53\times {10}^{11}{N/m}^3$

Q. A bicycle is being peddelled, then force of friction acts

1. on front wheel in forward direction.
2. on back wheel in backward direction.
3. on front wheel in backward direction .
4. on back wheel in forward direction.

Q. Three identical rods are joined and hinged at A as shown. If the angle made by the rod AB with vertical in equilibrium is $\theta$, then $\theta$ is

1. $30°$
2. $60°$
3. $37°$
4. $53°$

Q. A ruler scale is balanced with two fingers, $F_{1}and{F}_2$ at a separation 20 cm and 40 cm from O respectively. If the person balancing the ruler tries to bring his fingers closer to the centre, which finger will slide first?

1. $F_1$
2. $F_2$
3. Both simultaneously
4. Insufficient data

Q. Find the maximum magnitude of the attraction force.

1. $F_{max}=-\frac{b^3}{27a^2}$
2. $F_{max}=\frac{b^3}{27a^2}$
3. $F_{max}=3\frac{b^3}{27a^2}$
4. $F_{max}=-3\frac{b^3}{27a^2}$

Q.

A uniform solid cylinder of mass 'm' can rotate freely about its axis which is kept horizontal. A particle of mass $m_0$ hangs from the end of a light string wound round the cylinder. When the system is allowed to move, the acceleration with which the particle descends is

1. $\frac{2m_{0}g}{m_0+2m}$
2. $\frac{2m_{0}g}{m+2m_0}$
3. $\frac{m_{0}g}{m+m_0}$
4. $\frac{2m_{0}g}{m+2m_0}$

Q. Find out positions of unstable equilibrium.

1. B
2. D
3. F
4. A

Q. A square plate of side '4M' has uniform mass density and hinged at the midpoint of one of its edge as shown in figure. What will be the torque due to gravity on it about the hinged point A? $(M=20kg;g=\frac{10m}{s^2})$

1. 200 N-m
2. 100 N-m
3. 400 N-m
4. 300 N-m