Laws of Motion

A body of mass 'm' is launched up on a rough inclined plane making an angle of 30\(^\circ\) with the horizontal. The coefficient of friction between the body and plane is \({{\sqrt x } \over 5}\) if the time of ascent is half of the time of...

When a body slides down from rest along a smooth inclined plane making an angle of 30\(^\circ\) with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and throug...

An object of mass 'm' is being moved with a constant velocity under the action of an applied force of 2N along a frictionless surface with following surface profile.The correct applied force vs distance graph will be :

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 kg, M = 16 kg Assume all the surfaces shown in the figure to be ...

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10 m/s and it slows down with uniform deceleration, then th...

Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is \({3 \over 7}\). Then the maximum horizontal force that can be applied o...

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its ...

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction \({1 \over {\sqrt 3 }}\). It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________...

A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle \(\theta\) as shown in figure. The coefficient of kinetic friction is \(\mu\)k. then, the block's acceleration 'a' is given by :(g is accelerat...

A body of mass 2 kg moves under a force of \(\left( {2\widehat i + 3\widehat j + 5\widehat k} \right)\)N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is _____________. (R...

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied
horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45o
with the vertical. Then F equal : (Take g = 10 m...

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts
slipping after it is at height h from the bottom. If the coefficient of friction between the ground and
the insect is 0.75, then h is :
(g...

A particle moving in the xy plane experiences a velocity dependent force
\(\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)\)
, where vx
and vy
are the x and y components of its velocity \(\overrightarrow v\)
. If ...

A spaceship in space sweeps stationary
interplanetary dust. As a result, its mass
increases at a rate \({{dM\left( t \right)} \over {dt}}\) = bv2(t), where v(t) is
its instantaneous velocity. The instantaneous
acceleration of the satellite ...

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv2
where v is its speed. The maximum height attained by the ball is :

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, ...

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45o at the roof point. If the suspended mass is at equilibrium, the magnitude of...

A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of stat...

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched
lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constant, k1 and
k2 will be :

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an
angle of 30o with the horizontal, as shown in the figures. The coefficient of friction between the block and
floor is \(\mu\) = 0.2....

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle \(\theta\) with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \(\theta\) is -

A ball is thrown upward with an initial velocity
V0 from the surface of the earth. The motion
of the ball is affected by a drag force equal to
m\(\gamma\)u2 (where m is mass of the ball, u is its
instantaneous velocity and \(\gamma\) is a...

Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applie...

A bullet of mass 20 g has an initial speed of 1 ms–1
, just before it starts penetrating a mud wall of thickness
20 cm. If the wall offers a mean resistance of 2.5 × 10–2 N, the speed of the bullet after emerging from the
other side of the ...

A given object takes n times more time to slide down a \({45^ \circ }\) rough inclined plane as it takes to slide down a perfectly smooth \({45^ \circ }\) incline. The coefficient of kinetic friction between the object and the incline is :

A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of \({30^o}\). The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible
string over a frictionless pulley, are moving as shown in the figure. The
coefficient of friction of horizontal surface is 0.15. The minimum
weight m that should be put on to...

A rocket is fired vertically from the earth with an acceleration of 2g, where g is the
gravitational acceleration. On an inclined plane inside the rocket, making an angle \(\theta\) with the horizontal, a point object of mass m is kept. Th...

A particle of mass m is acted upon by a force F given by the empirical law
F =\({R \over {{t^2}}}\,v\left( t \right).\) If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

Given in the figure are two blocks \(A\) and \(B\) of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force \(F\) as shown. If the coefficient of friction between the blocks is 0.1 and between block \(B\) an...

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

A particle of mass \(m\) is at rest at the origin at time \(t=0.\) It is subjected to a force \(F\left( t \right) = {F_0}{e^{ - bt}}\) in the \(x\) direction. Its speed \(v(t)\) is depicted by which of the following curves?

Two fixed frictionless inclined planes making an angle \({30^ \circ }\) and \({60^ \circ }\) with the vertical are shown in the figure. Two blocks \(A\) and \(B\) are placed on the two planes. What is the relative vertical acceleration of ...

A block of mass \(m\) is connected to another block of \(mass\) \(M\) by a spring (massless) of spring constant \(k.\) The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a c...

A smooth block is released at rest on a \({45^ \circ }\) incline and then slides a distance \('d'\). The time taken to slide is \('n'\) times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

Consider a car moving on a straight road with a speed of \(100\) \(m/s\). The distance at which car can be stopped is \(\left[ {{\mu _k} = 0.5} \right]\)

A block is kept on a frictionless inclined surface with angle of inclination \('\,\alpha \,'.\) The incline is given an acceleration \(a\) to keep the block stationary. Then \(a\) is equal to

A particle of mass 0.3 kg subjected to a force \(F=-kx\) with \(k=15\) \(N/m\). What will be its initial acceleration if it is released from a point 20 cm away from the origin?

Two masses \({m_1} = 5kg\) and \({m_2} = 4.8kg\) tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? \(\left( {g = 9.8m/{s^2}} \right)\)

A block rests on a rough inclined plane `making an angle of \({30^ \circ }\) with the horizontal. The coefficient of static friction between the block and the plane is \(0.8.\) If the frictionless force on the block is \(10\) \(N,\) the mas...

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

A marble block of mass \(2\) \(kg\) lying on ice when given a velocity of \(6\) \(m/s\) is stopped by friction in \(10\) \(s.\) Then the coefficient of friction is

Three forces start acting simultaneously on a particle moving with velocity, \(\overrightarrow v \,\,.\) These forces are represented in magnitude and direction by the three sides of a triangle \(ABC\). The particle will now move with veloc...

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 \(5 m/{s^2}\), the reading of the sp...

A light spring balance hangs from the hook of the other light spring balance and a block of mass \(M\) \(kg\) hangs from the former one. Then the true statement about the scale reading is

A rocket with a lift-off mass \(3.5 \times {10^4}\,\,kg\) is blasted upwards with an initial acceleration of \(10m/{s^2}.\) Then the initial thrust of the blast is

A horizontal force of \(10\) \(N\) is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is \(0.2\). The weight of the block is

One end of a mass-less rope, which passes over a mass-less and friction-less 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 accelera...

Two forces are such that the sum of their magnitudes is \(18\) \(N\) and their resultant is \(12\) \(N\) which is perpendicular to the smaller force. Then the magnitudes of the forces are

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...