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What is the maximum value of the force F such that the block shown in the arrangement, does not move?

(1) 20 N
(2) 10 N
(3) 12 N
(4) 15 N

A block P of mass m is placed on a horizontal frictionless plane.  A second block of same mass m is  placed on it and  is connected to a spring of spring constant k, the two blocks are pulled by distance A.  Block Q oscillates without slipping.  What is the maximum value of fricitonal force between the two blocks.

(1) kA / 2
(2) kA
(3) ${\mu }_{s}mg$
(4) zero

A particle moves in the X-Y plane under the influence of a force such that its linear momentum is $\overrightarrow{p}\left(t\right)=A\left[\hat{i}\cos \left(kt\right)-\hat{j}\sin \left(kt\right)\right]$ where A and k are constants.  The angle between the force and the momentum is
(1) 0$°$
(2) 30$°$
(3) 45$°$
(4) 90$°$

A smooth block is released at rest on a 45$°$ incline and then slides a distance 'd'.  The time taken to side is 'n' times as much to slide on rough incline than on a smooth incline.  The coefficient of friction is
(1) ${\mu }_k=\sqrt{1-\frac{1}{n^2}}$
(2) ${\mu }_k=1-\frac{1}{n^2}$
(3) ${\mu }_s=\sqrt{1-\frac{1}{n^2}}$
(4) ${\mu }_s=1-\frac{1}{n^2}$

A block of mass m is placed on a surface with a vertical cross section given by $y=\frac{x^3}{6}$.  If the coefficient of friciton is 0.5, the maximum height above the ground at which the block can be placed without slipping is:
(1) $\frac{1}{6}m$
(2) $\frac{2}{3} m$
(3) $\frac{1}{3} m$
(4) $\frac{1}{2} m$

A point particle of mass m, moves long the uniformly rough track PQR as shown in the figure.  The coefficient of friction, between the particle and the rough track equals $\mu$.  The particle is released, from rest from the point P and it comes to rest at a point R.  The energies lost by the ball over the parts PQ and QR of the track are equal to each other and no energy is lost when particle  changes direction from PQ to QR.
The value of the coefficient of friciton $\mu$ and the distance x (=QR) are respectively close to:

(1) 0.29 and 3.5 m
(2) 0.29 and 6.5 m
(3) 0.2 and 6.5 m
(4) 0.2 and 3.5 m

A particle of mass m is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal.  At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle which was thrown vertically upward from the ground with the same initial speed $u_0$.  The angle that the composite system makes with the horizontal immediately after the collision is
(1) $\frac{\mathrm{\pi }}{4}$
(2) $\frac{\mathrm{\pi }}{4}+\alpha$
(3) $\frac{\mathrm{\pi }}{2}-\alpha$
(4) $\frac{\mathrm{\pi }}{2}$

A ball hits the floor and rebounds after an inelastic collision.  In this case.
(1) the momentum of the ball just after the collision is the same as that just before the collision.
(2) the mechanical energy of the ball remains the same in the collision.
(3) the total momentum of the ball and the earth is conserved.
(4) the total energy of the ball and the earth is not conserved.

Two blocks A and B, each of mass m, are connected by a massless spring of natural length L and spring constant K.  The blocks are initially resting on a smooth horizontal floor with the spring at its natural length, as shown in fig.  A third identical block C, also of mass m, moves on the floor with a speed v along the line joining A and B and collides elastically with A. Then

(1) the kinetic energy of the A-B system at maximum compression of the spring is zero.
(2) the kinetic energy of the A-B system at maximum compression of the spring, is $m{v}^2/8$
(3) the maximum compression of the spring is $v\sqrt{m/K}$
(4) the maximum compression of the spring is $v\sqrt{m/2K}$

This question has statement I and statement II of the four choices given after statements, choose the one that best describes the two statements.
Statement I: A point particle of mass m moving with speed v collides with stationary point particle of mass M.  If the maximum energy loss possible is given as $f\left(\frac{1}{2}m{v}^2\right)$ then $f=\left(\frac{m}{M+m}\right)$
Statement II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.
(1) Statement I is true, Statement  II is true , Statement II is the correct explanation of Statement I.
(2) Statement I is true, Statement II is true, Statement II is not the correct explanation of Statement II
(3) Statement I is true, Statement II is false
(4) Statement I is false, Statement II is true.

A particle of mass m moving in the x direction with speed 2 v is hit by another particle of mass 2 m moving in the y direction with speed v. If the collision is perfectly inelastic the percentage loss in the energy during the collision is close to:
(1) 56%
(2) 62%
(3) 44%
(4) 50%

A spring balance is attached to the ceiling of a lift.  A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary.  If the lift moves downward with an acceleration of 5 m/$s^2$, then reading of the spring balance will be
(1) 24 N
(2) 74 N
(3) 15 N
(4) 49 N

When forces $F_1, F_2, F_3$are acting on a particle of mass m such that $F_2 and F_3$ are mutually perpendicular, then the particle remains stationary.  If the force $F_1$ is now removed then the acceleration of the particle is
(1) $F_1/m$
(2) $F_2{F}_3/m{F}_1$
(3) $\left(F_2-F_3\right)/m$
(4) $F_2/m$

A light string passing over a smooth light pulley connects two blocks of masses $m_1 and m_2$ (vertically).  If the acceleration of the system is g / 8,then the ratio of the masses is
(1) 8 : 1
(2) 9 : 7
(3) 4 : 3
(4) 5 : 3

A rocket with a lift-off mass $3.5\times {10}^4$ kg is blasted upwards with an initial accelerationof 10 m/$s^2$.  Then the initial thrust of the blast is
(1) $3.5\times {10}^5 N$
(2) $7.0\times {10}^5 N$
(3) $14.0\times {10}^5 N$
(4) $1.75\times {10}^5 N$