Question 1 :
A body is projected vertically upwards with a velocity {tex} u , {/tex} after time {tex} t {/tex} another body is projected vertically upwards from the same point with a velocity {tex} v , {/tex} where {tex} v < u {/tex}. If they meet as soon as possible, then choose the correct option

Question 2 :
A {tex} 2 \mathrm { m } {/tex} wide truck is moving with a uniform speed {tex} v _ { 0 } = 8 \mathrm { m } / \mathrm { s } {/tex} along a straight horizontal road. A pedestrain starts to cross the road with a uniform speed {tex} v {/tex} when the truck is {tex}4 \mathrm { m } {/tex} away from him. The minimum value of {tex} v {/tex} so that he can cross the road safely is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e0dc657e50f934b847a5a4c">

Question 3 :
A balloon starts rising from the surface of the earth. The ascension rate is constant and equal to {tex} v _ { 0 } {/tex}. Due to the wind the balloon gathered the horizontal velocity component {tex} v _ { x } = a y , {/tex} where {tex}a{/tex} is a constant and {tex} y {/tex} is the height of ascent. The tangential, acceleration of the balloon is

Question 4 :
A projectile is thrown in the upward direction making an angle of {tex} 60 ^ { \circ } {/tex} with the horizontal direction with a velocity of {tex} 147 \ \mathrm { ms } ^ { - 1 } . {/tex} Then the time after which its inclination with the horizontal is {tex} 45 ^ { \circ } , {/tex} is

Question 5 :
A particle moves in the {tex} \mathrm { X } - \mathrm { Y } {/tex} plane with a constant acceleration {tex} 1.5 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} in the direction making an angle of {tex} 37 ^ { \circ } {/tex} with the {tex} \mathrm { X } {/tex} -axis. At {tex} \mathrm t = 0 {/tex} the particle is at the origin and its velocity is {tex} 8.0 \mathrm { m } / \mathrm { s } {/tex} along the {tex} \mathrm { X } {/tex}-axis. Find the position of the particle at {tex} \mathrm t = 4.0 \mathrm { s } {/tex}.

Question 6 :
A circular turn table has a block of ice placed at its centre. The system rotates with an angular speed {tex} \omega {/tex} about an axis passing through the centre of the table. If the ice melts on its own without any evaporation, the speed of rotation of the system<br>

Question 7 :
A gymnast takes turns with her arms and legs stretched. When she pulls her arms and legs in

Question 8 :
A ring of mass {tex} m {/tex} and radius {tex} R {/tex} has four particles each of mass {tex} m {/tex} attached to the ring as shown in figure. The centre of ring has a speed {tex} v _ { 0 } {/tex} . The kinetic energy of the system is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5d5e845a06864d5bec7be707"><br>

Question 9 :
A circular disc of radius {tex} R {/tex} is removed from a bigger circular disc of radius {tex} 2 \mathrm { R } {/tex} such that the circumferences of the discs coincide. The centre of mass of the new disc is {tex} \alpha / \mathrm { R } {/tex} form the centre of the bigger disc. The value of {tex} \alpha {/tex} is

Question 10 :
A wheel of radius {tex} 1 \mathrm { m } {/tex} rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

Question 11 :
A bullet is fired from a gun. The force on the bullet is given by {tex} F = 600 - 2 \times 10 ^ { 5 } t {/tex} where {tex}F{/tex} is in newton and {tex}t{/tex} in second. The force on the bullet becomes zero as soon as it leaves the barrel. What is the average impulse imparted to the bullet?

Question 12 :
A particle of mass {tex} m {/tex} rotates with a uniform angular speed {tex} \omega . {/tex} It is viewed from a frame rotating about the z-axis with a uniform angular velocity {tex} \omega _ { 0 } {/tex}. The centrifugal force on the particle is:

Question 13 :
In the diagram shown, friction is completely absent. If a force {tex} F {/tex} has been applied on the wedge such that it moves with a constant velocity than value of normal reaction {tex} N {/tex} is<br> <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/NEET/5e105321de596850506e3835' />

Question 14 :
Two identical smooth surfaced solid cylinders of radius r are placed touching along their lengths on a horizontal surface. A third cylinder of same material but twice the radius of that of the cylinders is placed lengthwise on them so that the system remains at rest. If all three cylinders have the same length, then minimum value of the coefficient of friction between smaller cylinders and the surface is:

Question 15 :
A weight {tex} W {/tex} is supported by two cables as shown. The tension in the cable making angle {tex} \theta {/tex} with horizontal will be the minimum when the value of {tex} \theta {/tex} is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NEET/5e101dcf4faa335027dc7aed"><br>

Question 16 :
A block of mass 2 kg rests on a rough inclned plane making am angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plans is 0.7. The frictional force on the block is $(g = 9.8 m/s^2)$ :

Question 18 :
A mass of 1 kg is suspended by a thread. It is <br> (i) lifted up with an acceleration {tex} 4.9 \mathrm { m } / \mathrm { s } ^ { 2 } , {/tex} <br>(ii) lowered with an acceleration {tex} 4.9 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex}. <br>The ratio of the tensions is

Question 19 :
Two bodies of masses {tex} 1 \mathrm { kg } {/tex} and {tex} 2 \mathrm { kg } {/tex} moving with same velocities are stopped by the same force. Then the ratio of their stopping distances is

Question 20 :
Sand is being dropped on a conveyor belt at the rate of M kg/s. The force (in N) necessary to keep the belt moving with a constant velocity of v m/s will be:

Question 21 :
One man takes {tex} 1 \mathrm { min } {/tex}. to raise a box to a height of {tex}1{/tex} metre and another man takes {tex} 1 / 2 \mathrm { min } {/tex}. to do so. The energy of the

Question 22 :
In elastic collision, {tex} 100 \% {/tex} energy transfer takes place when

Question 23 :
If two like charged particles are brought near one another, the potential energy of the system will

Question 24 :
An athlete in the olympic games covers a distance of {tex} 100 \mathrm { m } {/tex} in {tex} 10 \mathrm { s } {/tex}. His kinetic energy can be estimated to be in the range

Question 25 :
A boy pushes a toy box {tex} 2.0 \mathrm { m } {/tex} along the floor by means of a force of {tex} 10 \mathrm { N } {/tex} directed downward at an angle of {tex} 60 ^ { \circ } {/tex} to the horizontal. The work done by the boy is

Question 26 :
The work done on a particle of mass $m$ by a force $K \left[\dfrac{x}{(x<br>^{2}+y^{2})^{3/2}}\hat{i}+\dfrac{y}{(x^{2}+y^{2})^{3/2}}\hat{j} \right] $, where $K$ being a constant of appropriate dimensions, when the particle is taken from the point $(a,\ 0)$to the point $(0,\ a)$along a circular path of radius $a$ about the origin in the x-y plane is:<br>

Question 27 :
A bomb of mass {tex}9 \mathrm{kg}{/tex} explodes into the pieces of masses {tex} 3 \mathrm { kg } {/tex} and {tex} 6 \mathrm { kg } {/tex}. The velocity of mass {tex} 3 \mathrm { kg } {/tex} is {tex} 16 \mathrm { m } / \mathrm { s } {/tex}. The kinetic energy of mass {tex} 6 \mathrm { kg } {/tex} in joule is

Question 28 :
A force {tex} F = - K ( y \hat { i } + x \hat { j } ) {/tex} (where {tex} K {/tex} is a positive constant) acts on a particle moving in the {tex} x y {/tex} plane. Starting from the origin, the particle is taken along the positive {tex} x {/tex} axis to the point {tex} ( a , 0 ) , {/tex} and then parallel to the {tex} y {/tex} axis to the point {tex} ( a , a ) , {/tex} The total work done by the force {tex} F {/tex} on the particle is

Question 29 :
A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

Question 30 :
A mass of {tex} 20 \mathrm { kg } {/tex} moving with a speed of {tex} 10 \mathrm { m } / \mathrm { s } {/tex} collides with another stationary mass of {tex} 5 \mathrm { kg } {/tex}. As a result of the collision, the two masses stick together. The kinetic energy of the composite mass will be