A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is
A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is
- [NEET 2018]
- A
$a = \frac{g}{{cosec\theta }}$
- B
$a = \frac{g}{{sin\theta }}$
- C
$a=g tan$$\;\theta $
- D
$a=g cos $ $\theta $
Similar Questions
A block of mass $m_1=1 \ kg$ another mass $m_2=2 \ kg$, are placed together (see figure) on an inclined plane with angle of inclination $\theta$. Various values of $\theta$ are given in List $I$. The coefficient of friction between the block $m _1$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m _2$ and the plane are equal to $\mu=0.3$. In List $II$ expression for the friction on block $m _2$ given. Match the correct expression of the friction in List $II$ with the angles given in List $I$, and choose the correct option. The acceleration due to gravity is denoted by $g$.
[Useful information : $\tan \left(5.5^{\circ}\right) \approx 0.1 ; \tan \left(11.5^{\circ}\right) \approx 0.2 ; \tan \left(16.5^{\circ} \approx 0.3\right)$ ]
List $I$
List $II$
$P.\quad$ $\theta=5^{\circ}$
$1.\quad$ $m _2 g \sin \theta$
$Q.\quad$ $\theta=10^{\circ}$
$2.\quad$ $\left(m_1+m_2\right) g \sin \theta$
$R.\quad$ $\theta=15^{\circ}$
$3.\quad$ $\mu m _2 g \cos \theta$
$S.\quad$ $\theta=20^{\circ}$
$4.\quad$ $\mu\left(m_1+m_2\right) g \cos \theta$
A block of mass $m_1=1 \ kg$ another mass $m_2=2 \ kg$, are placed together (see figure) on an inclined plane with angle of inclination $\theta$. Various values of $\theta$ are given in List $I$. The coefficient of friction between the block $m _1$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m _2$ and the plane are equal to $\mu=0.3$. In List $II$ expression for the friction on block $m _2$ given. Match the correct expression of the friction in List $II$ with the angles given in List $I$, and choose the correct option. The acceleration due to gravity is denoted by $g$.
[Useful information : $\tan \left(5.5^{\circ}\right) \approx 0.1 ; \tan \left(11.5^{\circ}\right) \approx 0.2 ; \tan \left(16.5^{\circ} \approx 0.3\right)$ ]
| List $I$ | List $II$ |
| $P.\quad$ $\theta=5^{\circ}$ | $1.\quad$ $m _2 g \sin \theta$ |
| $Q.\quad$ $\theta=10^{\circ}$ | $2.\quad$ $\left(m_1+m_2\right) g \sin \theta$ |
| $R.\quad$ $\theta=15^{\circ}$ | $3.\quad$ $\mu m _2 g \cos \theta$ |
| $S.\quad$ $\theta=20^{\circ}$ | $4.\quad$ $\mu\left(m_1+m_2\right) g \cos \theta$ |
- [IIT 2014]
Two blocks $A$ and $B$ of masses $3\,m$ 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
Two blocks $A$ and $B$ of masses $3\,m$ 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
- [NEET 2017]
A frictionless cart $A$ of mass $100\ kg$ carries other two frictionless carts $B$ and $C$ having masses $8\ kg$ and $4\ kg$ respectively connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart so that smaller cart do not move relative to it .......... $N$
A frictionless cart $A$ of mass $100\ kg$ carries other two frictionless carts $B$ and $C$ having masses $8\ kg$ and $4\ kg$ respectively connected by a string passing over a pulley as shown in the figure. What horizontal force $F$ must be applied on the cart so that smaller cart do not move relative to it .......... $N$
A system to $10$ 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 $7^{th}$ and $8^{th}$ ball is $N$ when $6^{th}$ ball just leaves the table.
A system to $10$ 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 $7^{th}$ and $8^{th}$ ball is $N$ when $6^{th}$ ball just leaves the table.
- [JEE MAIN 2022]
A block of mass $M$ is at rest on a plane surface inclined at an angle $\theta$ to the horizontal. The magnitude of force exerted by the plane on the block is
A block of mass $M$ is at rest on a plane surface inclined at an angle $\theta$ to the horizontal. The magnitude of force exerted by the plane on the block is
- [KVPY 2009]