Centre of Gravity

Q.

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick?

Q.

A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.

Q. Assertion:The de Broglie equation has significance for any microscopic or sub -microscopic particles. Reason:The de Broglie wavelength is inversely proportional to the mass of the object if velocity s constant.

Q.

Two small kids weighing 10 kg and 15 kg are trying to balance a see saw of total length 5 m, with fulcrum at the centre. If one of the kids is sitting at the end, the other should sit at ____________

1. 1.5 m from centre

2. 1.6 m from centre

3. 1.7 m from centre

4. 1.8 m from centre

Q.

The block shown in the figure is in equilibrium. Find acceleration of the block just after the string is cut.

1. None

2. 

3. 

4. 

Q. a long horizontal rod with length along north-south direction falls under gravity. the potential diff across two ends is (inclide earths field) a)be zero b)be cons†an t c)increase with time d)decrease woth tim

Q.

Find the ratio of the weights, as measured by a spring balance, of a 1 kg block of iron and a 1 kg block of wood. Density of iron = 7800 kg $m^{-3}$, density of wood = 800 kg $m^{-}3$ and density of air = 1.293 kg $m^{-3}$.

Q. A weight $W$ is supported by two strings inclined at ${60}^{\circ }$ and ${30}^{\circ }$ to vertical. The tensions in the strings are $T_1$ and $T_2$ as shown. If these tensions have to be determined in terms of $W$ using a triangle of forces, then which of the following triangles should be drawn ?
(The blocks in equilibrium)

1. 
2. 
3. 
4. 

Q. A uniform meter scale can be balanced at the $70.0cm$ mark when a mass $0.05kg$ is hung from the $94.0cm$ mark. Find the mass of the metre scale :

1. $6kg$
2. $0.06kg$
3. $0.07kg$
4. $60kg$

Q. A small ball of mass M = 1 kg is attached to two identical springs of constant 100 N/m, which are attached to floor and roof. The springs are initially unstretched. By what distance ball down to attain equilibrium? (in cm) ___

Q. Two point masses of mass 2 kg and 6 kg are located such that their centre of mass is situated at a distance of 9 m from 2 kg mass. The separation between the two masses is

2 kg व 6 kg द्रव्यमान के दो बिन्दु द्रव्यमान इस प्रकार स्थित हैं कि इनका द्रव्यमान केन्द्र 2 kg द्रव्यमान से 9 m की दूरी पर स्थित हो। दोनों द्रव्यमानों के मध्य दूरी है

1. 2 m
2. 10 m
3. 12 m
4. 6 m

Q. A block of mass $10kg$ is moving in $x$-direction with a constant speed of $10m/s$. It is subjected to a retarding force $F=-0.1x$ joule / metre during its travel from $x=20$ meter to $x=30$ metre. Its final kinetic energy will be:

1. $250J$
2. $325J$
3. $625J$
4. $475J$

Q.

A non-uniform bar of weight W is suspended at rest by two strings of negligible weight as shown in Fig.7.39. The angles made by the strings with the vertical are ${36.9}^{\circ }$ and ${53.1}^{\circ }$ respectively. The bar is 2 m long. Calculate the distance d of the centre of gravity of the bar from its left end.

Q. A rope of length $10m$ and linear density $0.5kg/m$ is lying length wise on a smooth horizontal floor. It is pulled by a force of $25N$. The tension in the rope at a point $6m$ away from the point of application is

1. $15N$
2. $20N$
3. $10N$
4. $5N$

Q. The density of mass inside a solid sphere of radius $a$ is given by $\rho =\frac{{\rho }_{0}a}{r}$, where ${\rho }_0$ is the density at the surface and $r$ denotes the distance from the centre. Find the gravitational field due to this sphere at a distance $2a$ from its centre.

1. $\frac{1}{2}\pi G{\rho }_{0}a$
   
2. $\pi G{\rho }_{0}a$
   
3. $2\pi G{\rho }_{0}a$
   
4. $\frac{1}{4}\pi G{\rho }_{0}a$

Q. Two forces acting on a particle in opposite directions have a resultant of 10 kg wt. If they act at right angles to each other, the resultant is 60kg wt. The forces are (in kg. wt):

1. 47.4, 37.4
2. 40, 30
3. 60, 70
4. 14.3, 24.3

Q. A rod of length L and mass m pivoted about one end is oscillating in vertical plane. The period of oscillation for small amplitudes is

1. T = 2(L/3g)
2. T = 2(3L/2g)
3. T = 2(2L/3g)
4. T = 2(L/6g)

Q. A cart is moving horizontally along a straight line with constant speed $30{\text{ms}}^{-1}$. A particle is to be fired vertically upwards from the moving cart in such a way that it returns to the cart at the same point from where it was projected after the cart has moved $80\text{m}$. At what speed (relative to the cart) must the projectile be fired? (Take $g=10{\text{ms}}^{-1}$)

Q. Find the reading of the spring balance shown in figure The elevator is going up with an acceleration of $g/10$, the pulley and the string are light and the pulley is smooth.

Q. A man weighing 80 kg is standing on a trolley weighing 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley along the rails at a speed 1 ms${}^{-1}$ then after 4 second his displacement relative to the ground will be :

1. 3.0 m
2. 4.8 m
3. 5 m
4. 3.2 m

Q.

1. $2M$
2. $M/2$
3. $4M$
4. None of these

Q.

From a uniform disk of radius R, a circular hole of radius R/2 is cut out. The centre of the hole is at R/2 from the centre of the original disc. Locate the centre of gravity of the resulting flat body.

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.

1. True
2. False

Q. Two bodies of masses $4kg$ and $6kg$ are attached to the ends of a string passing over a pulley. The $4kg$ mass is attached to the table top by another string. The magnitude of tension in this string $T_1$ is equal to ($g=10m/s^2$)

1. 10 N
2. 10.6 N
3. 20 N
4. 25 N

Q. A small body of density ${\rho }^{\prime }$ is dropped from rest at a height $h$ into lake of density $\rho$, where $\rho >{\rho }^{\prime }$. Which of the follwing statements is/are neglected (neglected viscosity)?

1. The speed of the body just entering the lake is $\sqrt{2gh}$.
2. The body in the lake experience upward acceleration equal to $\left\{\right(\rho /{\rho }^{\prime })-1\}g$.
3. The maximum depth to which the body sinks in the lake is $h{\rho }^{\prime }/\left({\rho }^{\prime }/{\rho }^{\prime }\right)$.
4. The body does not come back to the surface of the lake.

Q. In the figure a smooth pulley of negligible weight is suspended by spring balance $1kg$ and $5kg$ are attached to the opposite ends of spring passing over pulley and move with acceleration because of gravity. During the motion, spring balance reads weight of ?

Q. Two particles $A$ and $B$ perform SHM along the same straight line with the same amplitude ${}^{\prime }a{}^{\prime },$ same frequency ${}^{\prime }f{}^{\prime }$ and same equilibrium position ${}^{\prime }O{}^{\prime }.$ The greatest distance between them is found to be $\frac{3a}{2}$. At some instant of time they have the same displacement from mean position. What is the displacement?

1. $\frac{a}{2}$
2. $\frac{a\sqrt{7}}{4}$
3. $\frac{3a}{4}$
4. $\frac{\sqrt{3}}{a2}$

Q. To the free of a string hanging from a rigid support, a block of mass m is hung and slowly allowed to come to its equilibrium position. Then the stretching in the spring is 'd'. If the same block is attached to the same spring and allowed to fall suddenly, the amount of stretching is (force constant k)

1. $\frac{mg}{3k}$
2. $4d$
3. $\frac{mg}{k}$
4. $2d$

Q. Mass become double and time becomes half , then 8 joule will be

Q. Four blocks and two springs are arranged as shown in $Fig.6.213$ the system at rest, determine the acceleration of all the loads immediately after the lower thread keeping the system in equilibrium has been cut. Assume that the threads are weightless, the mass of the pulley is negligible small, and there is no friction at the point of suspension.