Laws of Motion NEET Important Questions PDF Download

Q 1 :
A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at $30 °$ with the horizontal. The tension in the cord is 30 N. The acceleration of the box is (Take g = 10 ${ms}^{- 2}$ ) [2024]

2 ${ms}^{- 2}$
zero
0.1 ${ms}^{- 2}$
1 ${ms}^{- 2}$

1

2

3

4

(4)

From the given figure,

[IMAGE 34]----------------------------------

$m a = T - m g \sin θ$

$5 a = 30 - 5 \times 10 \times \frac{1}{2}$

$5 a = 30 - 25$

$a = 1$ ${m/s}^{2}$

Q 2 :
A block of mass 2 kg is placed on an inclined rough surface AC (as shown in figure) of coefficient of friction $μ$ . If g = 10 ${ms}^{- 2}$ , the net force (in N) on the block will be [2023]

[IMAGE 35]

$10 \sqrt{3}$
zero
10
20

1

2

3

4

(2)

The given parameters are, Coefficient of friction, $μ = \frac{1}{\sqrt{3}}$ and angle of friction is $30 ° .$

[IMAGE 36]---------------------------------

$F_{net} = m g \sin θ - μ m g \cos θ$

$= m g \sin 30 ° - μ m g \cos 30 °$

$= \frac{1}{2} m g - \frac{1}{\sqrt{3}} m g \frac{\sqrt{3}}{2} = \frac{1}{2} m g - \frac{1}{2} m g = 0$

Q 3 :
A small block slides down on a smooth inclined plane, starting from rest at time $t = 0$ . Let $S_{n}$ be the distance travelled by the block in the interval $t = n - 1$ to $t = n$ . Then, the ratio $\frac{S_{n}}{S_{n + 1}}$ is [2021]

$\frac{2 n}{2 n - 1}$
$\frac{2 n - 1}{2 n}$
$\frac{2 n - 1}{2 n + 1}$
$\frac{2 n + 1}{2 n - 1}$

1

2

3

4

(3)

The acceleration is $a = g \sin θ$

Initial velocity, $u = 0$

Distance travelled in $n^{th}$ second $S_{n^{t h}} = u + \frac{1}{2} a (2 n - 1)$

$S_{n^{t h}} = \frac{1}{2} a (2 n - 1)$ ...(i)

$S_{{(n + 1)}^{t h}} = \frac{1}{2} a [2 (n + 1) - 1]$ ...(ii)

On dividing eqn (i) by (ii), we get

$∴$ $\frac{S_{n^{t h}}}{S_{{(n + 1)}^{t h}}} = \frac{(2 n - 1)}{(2 n + 1)}$

Q 4 :
Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is [2020]

[IMAGE 37]

$g$
$g / 2$
$g / 5$
$g / 10$

1

2

3

4

(3)

[IMAGE 38]----------------------------

Given : $m_{1} = 4 kg, m_{2} = 6 kg$

From the diagram,

$T - m_{1} g = m_{1} a$ ...(i)

$m_{2} g - T = m_{2} a$ ...(ii)

Solving equation (i) and (ii)

$a = \frac{(m_{2} - m_{1}) g}{m_{2} + m_{1}} = \frac{(6 - 4) g}{10} = \frac{2}{10} g = \frac{g}{5}$

Q 5 :
A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $θ$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $θ$ for the block to remain stationary on the wedge is [2018]

[IMAGE 39]

$a = \frac{g}{c o s e c θ}$
$a = \frac{g}{\sin θ}$
$a = g \cos θ$
$a = g \tan θ$

1

2

3

4

(4)

[IMAGE 40]

In non-inertial frame,

$N \sin θ = m a$ ...(i)

$N \cos θ = m g$ ...(ii)

From (i) and (ii),

$\tan θ = \frac{a}{g}$

$\Rightarrow a = g \tan θ$

Q 6 :
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [2017]

[IMAGE 41]

$\frac{g}{3}, g$
$g, g$
$\frac{g}{3}, \frac{g}{3}$
$g, \frac{g}{3}$

1

2

3

4

(1)

[IMAGE 42]

Before the string is cut

$k x = T + 3 m g$ ...(i)

$T = m g$ ...(ii)

From eqns. (i) and (ii)

$k x = 4 m g$

Just after the string is cut

$T = 0$

$a_{A} = \frac{k x - 3 m g}{3 m}$

$a_{A} = \frac{4 m g - 3 m g}{3 m} = \frac{m g}{3 m} = \frac{g}{3}$

and $a_{B} = g$

Q 7 :
A balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$ ). How much mass should be removed from it so that it starts moving up with an acceleration $a$ ? [2014]

$\frac{2 m a}{g + a}$
$\frac{2 m a}{g - a}$
$\frac{m a}{g + a}$
$\frac{m a}{g - a}$

1

2

3

4

(1)

Let $F$ be the upthrust of the air. As the balloon is descending down with an acceleration $a$ ,

$∴$ $m g - F = m a$ ...(i)

[IMAGE 43]--------------------------------------------------

Let mass $m_{0}$ be removed from the balloon so that it starts moving up with an acceleration $a$ . Then,

$F - (m - m_{0}) g = (m - m_{0}) a$

$F - m g + m_{0} g = m a - m_{0} a$ ...(ii)

Adding equation (i) and equation (ii), we get

$m_{0} g = 2 m a - m_{0} a;$ $m_{0} g + m_{0} a = 2 m a$

$m_{0} (g + a) = 2 m a$

$m_{0} = \frac{2 m a}{a + g}$

Topic Question Set

Q 1 :
A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at $30 °$ with the horizontal. The tension in the cord is 30 N. The acceleration of the box is (Take g = 10 ${ms}^{- 2}$ ) [2024]

Q 2 :
A block of mass 2 kg is placed on an inclined rough surface AC (as shown in figure) of coefficient of friction $μ$ . If g = 10 ${ms}^{- 2}$ , the net force (in N) on the block will be [2023]

[IMAGE 35]

Q 3 :
A small block slides down on a smooth inclined plane, starting from rest at time $t = 0$ . Let $S_{n}$ be the distance travelled by the block in the interval $t = n - 1$ to $t = n$ . Then, the ratio $\frac{S_{n}}{S_{n + 1}}$ is [2021]

Q 4 :
Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is [2020]

[IMAGE 37]

Q 5 :
A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $θ$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $θ$ for the block to remain stationary on the wedge is [2018]

[IMAGE 39]

Q 6 :
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [2017]

[IMAGE 41]

Q 7 :
A balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$ ). How much mass should be removed from it so that it starts moving up with an acceleration $a$ ? [2014]

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Topic Question Set

Q 1 : A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at 30° with the horizontal. The tension in the cord is 30 N. The acceleration of the box is (Take g = 10 ms-2) [2024]

Q 2 : A block of mass 2 kg is placed on an inclined rough surface AC (as shown in figure) of coefficient of friction μ. If g = 10 ms-2, the net force (in N) on the block will be [2023] [IMAGE 35]

Q 3 : A small block slides down on a smooth inclined plane, starting from rest at time t=0. Let Sn be the distance travelled by the block in the interval t=n-1 to t=n. Then, the ratio SnSn+1 is [2021]

Q 4 : Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is [2020] [IMAGE 37]

Q 5 : A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration a towards the right. The relation between a and θ for the block to remain stationary on the wedge is [2018] [IMAGE 39]

Q 6 : Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [2017] [IMAGE 41]

Q 7 : A balloon with mass m is descending down with an acceleration a (where a<g). How much mass should be removed from it so that it starts moving up with an acceleration a ? [2014]

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Q 1 :
A box of mass 5 kg is pulled by a cord, up along a frictionless plane inclined at $30 °$ with the horizontal. The tension in the cord is 30 N. The acceleration of the box is (Take g = 10 ${ms}^{- 2}$ ) [2024]

Q 2 :
A block of mass 2 kg is placed on an inclined rough surface AC (as shown in figure) of coefficient of friction $μ$ . If g = 10 ${ms}^{- 2}$ , the net force (in N) on the block will be [2023]

[IMAGE 35]

Q 3 :
A small block slides down on a smooth inclined plane, starting from rest at time $t = 0$ . Let $S_{n}$ be the distance travelled by the block in the interval $t = n - 1$ to $t = n$ . Then, the ratio $\frac{S_{n}}{S_{n + 1}}$ is [2021]

Q 4 :
Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is [2020]

[IMAGE 37]

Q 5 :
A block of mass $m$ is placed on a smooth inclined wedge ABC of inclination $θ$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $θ$ for the block to remain stationary on the wedge is [2018]

[IMAGE 39]

Q 6 :
Two blocks A and B of masses 3m and m respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively [2017]

[IMAGE 41]

Q 7 :
A balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$ ). How much mass should be removed from it so that it starts moving up with an acceleration $a$ ? [2014]