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) $\mathrm{F}_1 / \mathrm{m}$
(2) $\mathrm{F}_2 \mathrm{~F}_3 / \mathrm{mF}_1$
(3) $\left(F_2 - F_3\right) / m$
(4) $\mathrm{F}_2 / \mathrm{m}$

Three identical blocks of masses $\mathrm{m} = 2 \mathrm{~kg}$ are drawn by a force $\mathrm{F} = 10.2 \mathrm{~N}$ with an acceleration of $0.6 \mathrm{~ms}^{-2}$ on a frictionless surface, then what is the tension (in N) in the string between the blocks $B$ and $C$?
(1) 9.2
(2) 7.8
(3) 4
(4) 9.8

One end of a massless rope, which passes over a massless and frictionless pulley $P$ is tied to a hook $C$ while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in $\mathrm{ms}^{-2}$) can a man of 60 kg climb on the rope?
(1) 16
(2) 6
(3) 4
(4) 8

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass m. If a force P is applied at the free end of the rope, the force exerted by the rope on the block is
(1) $\frac{\mathrm{Pm}}{\mathrm{M} + \mathrm{m}}$
(2) $\frac{\mathrm{Pm}}{\mathrm{M} - \mathrm{m}}$
(3) $P$
(4) $\frac{\mathrm{PM}}{\mathrm{M} + \mathrm{m}}$

If $t _ { 1 }$ and $t _ { 2 }$ are the times of flight of two particles having the same initial velocity $u$ and range R on the horizontal, then $t _ { 1 } ^ { 2 } + t _ { 2 } ^ { 2 }$ is equal to
(1) $\frac { u ^ { 2 } } { g }$
(2) $\frac { 4 u ^ { 2 } } { g ^ { 2 } }$
(3) $\frac { u ^ { 2 } } { 2 g }$
(4) 1

Two blocks of mass $M_1 = 20\mathrm{~kg}$ and $M_2 = 12\mathrm{~kg}$ are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is:
(1) 144 N
(2) 96 N
(3) 240 N
(4) 192 N

Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $\mathrm { M } = 2 \mathrm {~m}$, then the stress produced in the wire is:
(1) $\frac { 2 \mathrm { mg } } { 3 \mathrm {~A} }$
(2) $\frac { 4 \mathrm { mg } } { 3 \mathrm {~A} }$
(3) $\frac { \mathrm { mg } } { \mathrm { A } }$
(4) $\frac { 3 \mathrm { mg } } { 4 \mathrm {~A} }$

A body of mass 5 kg under the action of constant force $\vec{F} = F_x \hat{i} + F_y \hat{j}$ has velocity at $\mathrm{t} = 0 \mathrm{~s}$ as $\overrightarrow{\mathrm{v}} = (6\hat{\mathrm{i}} - 2\hat{\mathrm{j}}) \mathrm{m/s}$ and at $\mathrm{t} = 10 \mathrm{~s}$ as $\overrightarrow{\mathrm{v}} = +6\hat{\mathrm{j}} \mathrm{m/s}$. The force $\overrightarrow{\mathrm{F}}$ is:
(1) $(-3\hat{\mathrm{i}} + 4\hat{\mathrm{j}}) \mathrm{N}$
(2) $\left(-\frac{3}{5}\hat{i} + \frac{4}{5}\hat{j}\right) \mathrm{N}$
(3) $(3\hat{\mathrm{i}} - 4\hat{\mathrm{j}}) \mathrm{N}$
(4) $\left(\frac{3}{5}\hat{\mathrm{i}} - \frac{4}{5}\hat{\mathrm{j}}\right) \mathrm{N}$

A particle of mass m is moving in a straight line with momentum p. Starting at time $t = 0$, a force $F = k \mathrm { t }$ acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here $k$ is a constant. The value of T is
(1) $2\sqrt { \frac { k } { p } }$
(2) $2\sqrt { \frac { \mathrm { p } } { k } }$
(3) $\sqrt { \frac { 2k } { p } }$
(4) $\sqrt { \frac { 2p } { \mathrm { k } } }$

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \mathrm {~kg} , \quad M = 16 \mathrm {~kg}$ Assume all the surfaces shown in the figure to be frictionless.
(1) $\frac { 3 } { 5 } \mathrm {~g}$
(2) $\frac { 4 } { 3 } \mathrm {~g}$
(3) $\frac { 6 } { 5 } \mathrm {~g}$
(4) $\frac { 2 } { 3 } \mathrm {~g}$

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02. The acceleration of block is: (Given $g = 10 \mathrm{~m~s}^{-2}$.)
(1) $\frac{8}{11} \mathrm{~m~s}^{-2}$
(2) $1 \mathrm{~m~s}^{-2}$
(3) $\frac{1}{5} \mathrm{~m~s}^{-2}$
(4) $\frac{4}{5} \mathrm{~m~s}^{-2}$

A block of mass $M$ placed inside a box descends vertically with acceleration $a$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of $|a|$ will be
(1) $g$
(2) $\frac{3g}{4}$
(3) $\frac{g}{2}$
(4) $\frac{g}{4}$

A hanging mass $M$ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $2Mg$ force. In this situation, tension in the string is $\frac{x}{5}Mg$ for $x =$ $\_\_\_\_$. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given $g =$ acceleration due to gravity)

A system of 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7 ^ { \text {th} }$ and $8 ^ { \text {th} }$ ball is $\_\_\_\_$ N when $6 ^ { \text {th} }$ ball just leaves the table.

A body of mass 500 g moves along $x$-axis such that it's velocity varies with displacement $x$ according to the relation $v = 10 \sqrt { x } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ the force acting on the body is:
(1) 125 N
(2) 25 N
(3) 166 N
(4) 5 N

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in $\mathrm { m } \mathrm { s } ^ { - 2 }$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):
(1) 3
(2) 4
(3) 2
(4) 1.2

A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1\mathrm{~ms}^{-2}$. The action force of the system on the floor is equal to:
(1) 196 N
(2) 291 N
(3) 294 N
(4) 297 N

Three blocks $M_1, M_2, M_3$ having masses $4\mathrm{~kg}, 6\mathrm{~kg}$ and $10\mathrm{~kg}$ respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, $T_1$ when they are moving upward with acceleration of $2\mathrm{~ms}^{-2}$ is $\_\_\_\_$ $\mathrm{N}$ (if $\mathrm{g} = 10\mathrm{~m/s}^2$).