Calculation for Varying Direction

Q. A block of mass $m$ is suspended by a light thread from an elevator. The elevator is accelerating upward with a uniform acceleration $a$. The work done by tension on the block in $t$ seconds is $(u=0)$

1. $\frac{m}{2}(g+a)a{t}^2$
2. $\frac{m}{2}(g-a)a{t}^2$
3. $\frac{m}{2}ga{t}^2$
4. $0$

Q. A body at rest has mass $10\text{kg}$. It is moved by a horizontal force of $5\text{N}$ on a frictionless horizontal surface. The work done by the force in $8\text{s}$ is -

1. $\text{80 J}$
2. $\text{85 J}$
3. $\text{70 J}$
4. $\text{60 J}$

Q. A ball of mass $100\text{g}$ is under a force which causes a displacement $S$ in metres, given by the relation $S=t^3+t^2$ where $t$ is in seconds. Work done by the force in 3 seconds

1. $20\text{J}$
2. $54.45\text{J}$
3. $72.45\text{J}$
4. $36.55\text{J}$

Q. A simple pendulum is oscillating without damping.When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in

1. 
2. 
3. 
4. 

Q.

A simple pendulum has a time period exactly 2s when used in a laboratory at north pole. What will be the time period if the same pendulum is used in a laboratory at equator? Account for the earth's rotation only. Take g $\frac{Gm}{r^2}$ = 9.8 m/s² and radius of earth = 6400 km.

1. 2.004 seconds

2. 0.004 seconds

3. 4.004 seconds

4. 2 seconds

Q.

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

1. $\sqrt{u^2-2gL}$

2. $\sqrt{2gL}$
   

3. $\sqrt{2(u^2-2gL)}$

4. $\sqrt{u^2-gL}$

Q. A force $F=(10+0.5x)$ acts on a particle in the $x$ direction, where $F$ is in $\text{newton}$ and $x$ is in$\text{metre}$. Find the work done by this force during the displacement from $x=0$ to $x=2.0\text{m}$

1. $18\text{J}$
2. $19\text{J}$
3. $20\text{J}$
4. $21\text{J}$

Q. Under the action of a force, a body of mass $4\text{kg}$ moves along $x-$ axis, such that $x$ as a function of time is given by $x=\frac{t^3}{3}$, where all quantities are in $\text{SI}$ units. What is the work done in the first three seconds ?

1. $324\text{J}$
2. $162\text{J}$
3. $81\text{J}$
4. $9\text{J}$

Q. An elevator without a ceiling is ascending with a constant speed of $10m/s$. A boy on the elevator shoots a ball directly upward, from a height of $2.0m$ above te elevator floor. At this time the elevator floor is $28m$ above the ground. The initial speed of the ball with respect to the elevator is $20m/s$. (g= $10m/s^2$). What maximum height above the ground does the ball reach?

1. $45$
   
2. $75$
   
3. $30$
   
4. $90$
   

Q.

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

1. $\sqrt{u^2-2gL}$

2. $\sqrt{2gL}$
   

3. $\sqrt{u^2-gL}$

4. $\sqrt{2(u^2-2gL)}$

Q. A force of $15\text{N}$ acts on an object of mass $10\text{kg}$ for $12\text{s}$. The work done by this force is

1. $1525\text{J}$
2. $1620\text{J}$
3. $2000\text{J}$
4. $875\text{J}$

Q. A ball of mass $200$g falls of the ground from a height of $2.5$m and rises to a height of $0.4$m on hitting the ground. If the time of contact of the hall with the ground is $0.02$s, what is the force exerted by the ground on the ball? ($g=9.8m/s^2$)

1. $98.9N$
2. $111.9N$
3. $141.4N$
4. $125.6N$

Q. A ball of mass $2kg$ and another of mass $4kg$ are dropped together from a $60$ feet tall building. After a fall of $30$ feet each towards earth, their respective kinetic energies will be in the ratio of-

1. $1:4$
2. $1:2$
3. $1:\sqrt{2}$
4. $\sqrt{2}:1$

Q. Statement I :A small block of mass m is projected with some speed from point A on a smooth vertical tube track of small diameter as shown in Fig. 8.210. The vertical heights of points B and C from point of projection are $h_{B}and{h}_C$ such that $h_B=2h$ and $h_C=h.$ Then the minimum possible speed of the block at point C is $\sqrt{2gh}$ (where g is acceleration due to gravity).

Statement II . The minimum speed of the block at point C in situation given in Statement I depends on $h_B-h_C.$

1. Statement I is false, Statement II is true
2. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
3. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
4. Statement I is true, Statement II is false

Q. Statement I :A small block of mass m is projected with some speed from point A on a smooth vertical tube track of small diameter as shown in Fig. 8.210. The vertical heights of points B and C from point of projection are $h_{B}and{h}_C$ such that $h_B=2h$ and $h_C=h.$ Then the minimum possible speed of the block at point C is $\sqrt{2gh}$ (where g is acceleration due to gravity).

Statement II . The minimum speed of the block at point C in situation given in Statement I depends on $h_B-h_C.$

1. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
2. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
3. Statement I is true, Statement II is false
4. Statement I is false, Statement II is true

Q.

A stone tied to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position, and has a speed u. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

1. $\sqrt{u^2-2gL}$

2. $\sqrt{2gL}$
   

3. $\sqrt{u^2-gL}$

4. $\sqrt{2(u^2-2gL)}$

Q. A simple pendulum is oscillating without damping.When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in

1. 
2. 
3. 
4. 

Q. A ball of mass $100\text{g}$ is under a force which causes a displacement $S$ in metres, given by the relation $S=t^3+t^2$ where $t$ is in seconds. Work done by the force in 3 seconds

1. $72.45\text{J}$
2. $36.55\text{J}$
3. $20\text{J}$
4. $54.45\text{J}$

Q. A 1 kg mass falls from a height of 10 m into a sand box. What is the speed of the mass just before hitting the sand box? If it travels a distance of 2 cm into the sand box before coming to rest, what is the average retarding force?

1. $12m/s$ and $3600N$
2. $14m/s$ by $4900N$
3. $16m/s$ by $6400N$
4. $18m/s$ by $8100N$

Q. A body of mass $m$ is suspended as shown in figure , choose the incorrect statement regarding the case

1. Angular momentum is constant about O
2. Angular momentum is constant about C
3. Vertical component of of angular momentum about O is constant
4. magnitude of angular momentum about O is constant

Q. A stone is tied to a string of length ${}^{\prime }{\ell }^{\prime }$ and is whirled in a vertical circle with the other end of the string as the center. At a certain instant of time, the stone is at its lowest position and has a speed ${}^{\prime }{u}^{\prime }$. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is :

1. $\sqrt{u^2-g\ell }$
2. $u-\sqrt{u^2-2g\ell }$
3. $\sqrt{2g\ell }$
4. $\sqrt{2(u^2-g\ell )}$

Q. A simple pendulum is oscillating without damping.When the displacement of the bob is less than maximum, its acceleration vector $\overrightarrow{a}$ is correctly shown in

1. 
2. 
3. 
4. 

Q. Statement I :A small block of mass m is projected with some speed from point A on a smooth vertical tube track of small diameter as shown in Fig. 8.210. The vertical heights of points B and C from point of projection are $h_{B}and{h}_C$ such that $h_B=2h$ and $h_C=h.$ Then the minimum possible speed of the block at point C is $\sqrt{2gh}$ (where g is acceleration due to gravity).

Statement II . The minimum speed of the block at point C in situation given in Statement I depends on $h_B-h_C.$

1. Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
2. Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
3. Statement I is true, Statement II is false
4. Statement I is false, Statement II is true

Q. A ball of mass $100\text{g}$ is under a force which causes a displacement $S$ in metres, given by the relation $S=t^3+t^2$ where $t$ is in seconds. Work done by the force in 3 seconds

1. $72.45\text{J}$
2. $36.55\text{J}$
3. $20\text{J}$
4. $54.45\text{J}$

Q. A ball with a mass of 2 kg is swung in a circular path on a massless rope of length 0.5 m. If the balls speed is 1 m/s, what is the tension in the rope?

Q. Figure shows an elevator cabin, which is moving downwards with constant acceleration $a$. A particle is projected from corner $A$, directly towards diagonally opposite corner $C$. Then prove that
a. Particle will hit $C$ only when $a=g$
b. Particle will hit the wall $CD$ if $a<g$
c. Particle will hit the roof $BC$ if $a>g$.